Spock's journey, in order
To watch Spock's story in order, start with Discovery: Season 2, then Strange New Worlds: Season 1 and Strange New Worlds: Season 2. That's 16 out so far, about 148 hours, ending with Star Trek (2009).
Spock's story is the longest in Star Trek: Ethan Peck plays him before Kirk's time, Leonard Nimoy through the original series and films, and Zachary Quinto in the Kelvin timeline, where Nimoy's Spock appears too.
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Spock's story in order
Discovery: Season 2
Spock and his sister Michael Burnham.
Strange New Worlds: Season 1
Spock serves under Captain Pike.
Strange New Worlds: Season 2
Strange New Worlds: Season 3
Strange New Worlds: Season 4
The Original Series: Season 1
Leonard Nimoy's Spock, first officer to Kirk.
The Original Series: Season 2
The Original Series: Season 3
The Motion Picture
The Wrath of Khan
Spock's sacrifice.
The Search for Spock
Spock's return.
The Voyage Home
The Final Frontier
The Undiscovered Country
Spock opens peace talks with the Klingons.
The Next Generation: Season 5
Spock appears in the two-part episode 'Unification'.
Star Trek (2009)
An old Spock travels to the past and meets his younger self.
Questions
What order should I watch Spock's story in?
Start with Discovery: Season 2, then Strange New Worlds: Season 1 and Strange New Worlds: Season 2, and follow the list above: 16 in all, ending with Star Trek (2009).
How long does it take to watch all of Spock's story?
About 148 hours for the 16 out so far.
Where is Spock in The Next Generation?
In the Season 5 two-parter 'Unification', where Picard finds him working for peace on Romulus.
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