Fallout 4 Quests

Prologue
The prologue is set in the year 2077, and consists of a single quest, which does not appear in the player character's quest log.

Act 1
Act 1 begins when the Sole Survivor awakens in the year 2287, over 200 years after entering their cryo pod in Vault 111.

Act 2
The beginning of act 2 is heralded by the arrival of The Prydwen, and opens up the majority of the Brotherhood of Steel quests.

Act 3
Act 3 begins when the Sole Survivor first sets foot in The Institute.

At this point, the main quest's structure becomes similar to the one from Fallout: New Vegas. There are four different branches, one for each faction, and certain events in those quests can make certain factions hostile to the Sole survivor, thus locking them from those branches and failing all of that faction's on-going quests. In some situations, this can be delayed (or even accelerated) with certain actions or certain dialogue choices. Should the player decide to oppose The Institute by supporting any of the other three factions, the main quest ends with The Nuclear Option quest (there are actually three variants of the same quest, one for each faction opposing The Institute). However, should the player join and support The Institute, the main quest ends with the Nuclear Family quest.

The following quests become available after completing The Molecular Level:
 * Institutionalized (The Institute branch) - starts automatically
 * From Within (Brotherhood of Steel branch) - given by Elder Maxson if the player completed Show No Mercy, or is given automatically if the player used the Brotherhood of Steel to advance in The Molecular Level
 * Inside Job (The Minutemen branch) - given by Sturges if the player completed Old Guns, or is given automatically if the player used the Minutemen to advance in The Molecular Level
 * Underground Undercover (The Railroad branch) - given by Desdemona if the player joined the Railroad by completing the Tradecraft quest, or is given automatically if the player used the Railroad to advance in The Molecular Level

Side quests
These are non-affiliated side quests.

Miscellaneous quests
These quests are displayed under the section "Miscellaneous" of the Pip-Boy.

Unmarked quests
These are quests that can be completed for certain rewards, but do not appear in your Pip-Boy.

Companion quests
The following quests are given once the player gains enough affinity with a particular companion.

Settlement quests
In addition to the Help defend (settlement name) quests, there are a number of unmarked quests associated with settlements.

Automatron
These quests are only playable after Automatron has been installed. 

Far Harbor
These quests are only playable after Far Harbor has been installed. 

Nuka-World
These quests are only playable after Nuka-World has been installed. 