Fallout 4 Quests

Act one
Act one begins when the Sole Survivor awakens in the year 2287, 210 years after entering their cryo pod in Vault 111.

Act two
The beginning of act two is heralded by the arrival of the Prydwen, opening up the majority of the Brotherhood of Steel quests.

Act three
Act three begins when the Sole Survivor acquires the ability to fast-travel to and from the Institute at the end of Institutionalized. At this point, the main quest's structure splits into four different branches, one for each of the four main factions. Certain events in those factions' quests can make other 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 character 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 Sole Survivor join and support the Institute, the main quest ends with the Nuclear Family quest.

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

Secondary quests
These quests are not affiliated with any main faction.

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

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

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

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

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

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

Vault-Tec Workshop
These quests are only available after Vault-Tec Workshop has been installed. 

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