Here follows a chronological account of the most important wars, battles, sieges, falls and combats in The Silmarillion.
General ‘Wars and Battles’ timeline:

War of the Valar against Morgoth
War of Morgoth against the Elves of Beleriand (the First Battle)
The First Kinslaying (at Alqualondë)
Dagor-nuin-Giliath (Battle Under the Stars)
Dagor Aglareb (Glorious Battle)
Siege of Angband
Dagor Bragollach (Battle of the Sudden Flame)
Duel of Morgoth and Fingolfin
The song duel of Sauron and Finrod Felagund
Nirnaeth Arnoediad (Battle of Unnumbered Tears)
Fall of Nargothrond & Battle of Tumhalad
Fall of Doriath
The Second Kinslaying (at Doriath)
Fall of Gondolin
The Third Kinslaying (at Havens of Sirion)
War of Wrath

Second Age:
War of Sauron on Eregion
War of Ar-Pharazôn on Valinor (attempted)
Fall of Númenor
War of the Last Alliance (including the Battle of Dagorlad, the Siege of Barad-dûr, and the combat of Gil-Galad and Elendil against Sauron)

For Third Age, please see the timeline in LotR.

WARS

War of the Valar against Morgoth (Battle of the Powers)
– The Valar were concerned for the safety of the newly awakened Elves; they assaulted Morgoth’s servants and his first stronghold Utumno.The Valar won.
Result: Utumno destroyed; Morgoth imprisoned; many of his servants fled or hid.
You know it from: It is probable that this battle is meant when Théoden is likened to Oromë “in the battle of the Valar when the world was young”. (RotK)

War of Morgoth against the Elves of Beleriand (The First Battle)
– After stealing the Silmarils in Valinor, Morgoth escaped to Middle-earth to his fortress of Angband; shortly afterwards his orc army assailed the Elven realms and settlements; the Elves of Middle-earth were saved by the coming of the exiled Elves from Valinor.
Result: Orcs roamed Beleriand freely; the Girdle of Melian was created to protect Doriath so that none could enter the realm.

War of the Jewels – the generic name for the war between the Elves and Morgoth after the theft of the Silmarils; ends with the regaining of the Silmarils by the host of Valinor in the War of Wrath; most notable battles of this long struggle are [b]Dagor-nuin-Giliath (Battle Under the Stars), Dagor Aglareb (Glorious Battle), Dagor Bragollach (Battle of the Sudden Flame),[/b] and Nirnaeth Arnoediad (Battle of Unnumbered Tears).

Wars of Beleriand– generic name for the War of the Jewels plus the preceding War of Morgoth against the Elves of Beleriand (The First Battle)

War of Wrath– the battle/war that marks the end of the First Age
– The Valar agreed to aid the remnants of the free peoples of Middle-earth in their failing struggle against Morgoth; a great Valinorean army met Morgoth’s armies in the North of Beleriand; the hosts of Valinor won.
Result: Morgoth defeated and cast into the Void; most of his servants destroyed; the shape of Middle-earth was changed and Beleriand sunk into the Sea; the Exiled Elves were permitted to sail to Valinor; the faithful Men received the island of Númenor in return for their bravery.
You know it from: Elrond reminiscences on the splendour of the armies in this war at the Council. (FotR)

~SECOND AGE WARS~

War of Sauron on Eregion
– Sauron realised he would not be able to control the Elves through the Rings of Power and decided to destroy them and regain their Rings. He and his armies laid waste the land of Eregion (Hollin), where Sauron regained the Nine Rings; his armies got as far as Grey Havens. Sauron’s progress was stopped by the arrival of a mighty fleet from Númenor; he was defeated and driven back into Mordor. The Númenoreans and their allies won. Celebrimbor the maker of the Three Rings died in this war.
Result: Rivendell founded as a refuge; Eregion destroyed; the Three Rings hidden with Elven keepers.
You know it from: It is relayed during the Council. (FotR)

War of Ar-Pharazôn on Valinor (attempted)
– The last Númenorean king Ar-Pharazôn became corrupted by Sauron’s lies into believing that gaining dominion of Valinor would grant him immortality; a great fleet led by Ar-Pharazôn sailed for Valinor, reaching its shores and making an encampment there; both the army and Númenor were then destroyed as Ilúvatar intervened.
Result: the drowning of Númenor.

War of the Last Alliance
– Sauron began attacking Gondor, and Elendil and Gil-galad decided to march into war against him. The most notable events of this war are: Battle on Dagorlad before the Black Gate; several years lasting siege of the Dark Tower; the final combat of Sauron against Elendil and Gil-Galad on the slopes of Mt. Doom. The Last Alliance of Elves and Men won. Elendil, Gil-galad and Anárion died in this war.
Result: Sauron’s servants dispersed; Gondor and Arnor have peace for a long time.
You know it from: It is mentioned in LotR many times.

BATTLES

Dagor-nuin-Giliath (Battle Under the Stars) [‘dah-gor ‘nooin ‘gih-lee-ath]
– shortly after the first Exiles arrived from Valinor to Middle-earth, they were attacked by Morgoth’s orc army that was roaming the lands freely; the Elves won swiftly. The battle took place before the Moon and the Sun rose, hence the name. Fëanor the leader of the first Exiles died in this battle.

Dagor Aglareb (Glorious Battle) [‘dah-gor ‘ahg-lah-reb]
– Morgoth wished to test the strength and watchfulness of the Elves of Beleriand; his orc armies attacked several Elvish realms, but were quickly defeated and utterly destroyed.
[b]Result:[/b] the 400 years lasting Siege of Angband by the Elves begins; Morgoth attempts no further major battle until the B. of the Sudden Flame.

Dagor Bragollach (Battle of the Sudden Flame) [‘dah-gor brah-‘gol-lakh]
– Morgoth regained enough strength to assail the Elvish realms while most of the Elves were content keeping the Siege of Angband. Rivers of fire and poisonous smoke were released suddenly from Angband, destroying the plain before it; after that, dragons, balrogs, and orcs issued forth; the Elves and their Mannish allies lost the long battle that took place on several fronts. During this battle, Finrod Felagund gives his ring to the Man Barahir who saved his life. Two of Galadriel’s brothers (Angrod and Aegnor) died in this battle.
Result: End of Siege of Angband; Morgoth conquers and besieges some lands; Sauron settles in Tol Sirion and transforms it into the Isle of Werewolves that plays a role in the tale of Beren and Lúthien; the largest three Elven kingdoms – Doriath, Nargothrond and Gondolin – still stand.

Nirnaeth Arnoediad (Battle of Unnumbered Tears) [‘neer-nayeth ar-‘noi-dee-ahd]
– the Elves of Beleriand planned a decisive assault on Morgoth’s fortress; the initial strengths of the allies (most Elves, uncorrupted Men, Dwarves) and of Morgoth were almost equal, but treachery of some contingents of Easterling Men led to a swift victory of Morgoth’s army. Húrin father of Túrin was captured in this battle. Fingon the High King of the Noldor in Middle-earth and Huor father of Tuor died in this battle.
Result: Morgoth’s power stretches over the entire North and many other regions of Middle-earth; the lands where Tuor and Túrin were born are ruled by Easterling Men; the three major Elven realms –Gondolin, Nargothrond and Doriath- still stand, as do the southern lands; Elves begin to distrust most Men.

Battle of Tumhalad – a lesser battle; defeat of the armies of the Elven realm Nargothrond by Morgoth’s army in the valley of Tumhalad; Túrin Turambar fought for Nargothrond and Orodreth the king of Nargothrond died in this battle.
Result: End of the Realm of Nargothrond.

~ SECOND AGE BATTLES~

Battle of Dagorlad– a great battle on the plain of Dagorlad before the Black Gate of Mordor in which the Last Alliance defeated Sauron’s army and proceeded into Mordor; the victims of the battle were buried in where later the Dead Marshes would stretch.
You know it from: It is mentioned several times in LotR; Gollum talks of it in more detail in the Dead Marshes. (TTT)

SIEGES

First Age: Siege of Angband– siege of Morgoth’s fortress by the Elves of Middle-earth; lasted for cca 400 years, from The Glorious Battle until the Battle of the Sudden Flame.

Second Age: Siege of Barad-dûr– siege of the Dark Tower in Mordor by the Last Alliance; lasted several years; ends when Sauron himself issues from the Dark Tower.

COMBATS AND DUELS

Duel of Morgoth and Fingolfin
– Fingolfin, the High King of the Noldor in Middle-earth, was filled with despair after the disastrous Battle of the Sudden Flame; he rode to Angband alone and challenged Morgoth; he died in the combat although Morgoth was wounded.

The song duel of Sauron and Finrod Felagund
– Finrod, Beren and their company were intercepted by Sauron on their quest for the Silmaril; Finrod starts a duel with Sauron in songs of power; Sauron wins.
Result: Finrod, Beren and their companions imprisoned until they reveal their purpose.

~ SECOND AGE COMBATS~

Combat of Gil-Galad and Elendil against Sauron – takes place on the slopes of Mt Doom; the decisive moment of the War of the Last Alliance; Elendil and Gil-galad defeat Sauron but both die at his hand.
Result: Sauron is temporarily vanquished and disembodied when his finger with the One Ring is cut off by Isildur.
You know it from: It is spoken of in LotR, in greatest detail in Elrond’s account at the Council.

KINSLAYINGS

The First Kinslaying (at Alqualondë)– the slaying of many Sea Elves at Alqualondë (Swan Haven) in Valinor by followers of Fëanor, after the Sea Elves refused to lend their white ships so that Fëanor’s followers could pass over the Sea to Middle-earth.
Result: the kinslaying contributed to the closing of Valinor to the now exiled Elf hosts; upon hearing the news in his realm of Doriath in Middle-earth, Thingol –brother to the king of Alqualondë- denied entrance into his realm to those who took part in this deed.

The Second Kinslaying (at Doriath)– the slaying of many Doriath Elves by the Sons of Fëanor and their followers, after Dior -the new king of Doriath after the death of Thingol- refused to surrender the Silmaril he inherited from his parents Beren and Lúthien to the Sons of Fëanor, who were oath-bound to reclaim the Silmarils for their House. The Sons of Fëanor won, although three of them died. Dior and his wife were killed.
Result: utter ruin of Doriath; a few survivors escape with the Silmaril and the Sons of Fëanor do not regain it.

The Third Kinslaying (at Havens of Sirion) – the slaying of most of the Elves living in the Havens of Sirion (refugees from the fall of Doriath and fall of Gondolin) by the Sons of Fëanor and their followers, after Elwing their leader refused to surrender the Silmaril she inherited to the Sons of Fëanor, who were oath-bound to reclaim the Silmarils for their House. The Sons of Fëanor win although two of them die. Elwing escapes with the Silmaril, her twin sons Elrond and Elros are taken captive.
Result: destruction of the Havens; Elwing joins her husband Eärendil on his voyage to Valinor.

FALLS

Fall of Nargothrond– defeat of the army of Nargothrond in the Battle of Tumhalad, followed by the sacking of Nargothrond by Morgoth’s servants led by Glaurung the dragon.
You know it from: The falls of Nargothrond and Gondolin are mentioned in Gimli’s song of Moria, and by Galadriel when sharing a glimpse of her past with the Fellowship. (FotR)

Fall of Doriath – 1) death of Thingol king of Doriath at the hands of Dwarves, and the subsequent sack of his halls by a Dwarven army; followed in a few years by 2) the Second Kinslaying and the end of the realm of Doriath.

Fall of Gondolin– a quick destruction by Morgoth’s forces of the city of Gondolin whose location had been unknown to him for long, until revealed to him by a traitor; dragons and balrogs were used along with orcs to destroy the city with flame and force. Some of the people of Gondolin escaped through a secret passage leading into the surrounding mountains. Among the victims were Turgon the king of Gondolin, Ecthelion, Glorfindel, as well as Gothmog the lord of balrogs and Maeglin the traitor.
You know it from: it’s mentioned by Elrond when explaining his ancestry at the Council (FotR), and when explaining the history of the elvish blades from the troll-hoard to Gandalf and the Dwarves (The Hobbit)

~SECOND AGE FALLS~

Fall of Númenor– Eru Ilúvatar’s punishment for the audacity of the Númenoreans who dared attack Valinor; the entire island fell into an abyss that opened in the sea; Elendil and his people were saved from the Fall in their ships, and a fierce storm brought their ships to Middle-earth.
You know it from: Elrond talks about the Fall of Númenor at the Council.