/review is accessible to all users, but does not appear in the top bar until the 500 reputation milestone. While anybody can view recent reviews, the actual review queues are inaccessible until you gain the appropriate amount of reputation. The reputation requirements for each queue correspond to the reputation required to perform most of the actions in that queue, with the exception of the first and late posts that both require 500.
For reference, the current reputation thresholds and their linked privileges are as follows:
Note that on beta sites and non-designed sites, the reputation requirements for privileges and the
/review queue are lower. Also, on per-site metas and Meta Stack Exchange, the First Posts and Late Answers queues don't exist, so the review icon won't show up in the top bar on those sites until you have 2000 reputation.