To review (verb) means to analyze, inspect, evaluate.  (reviewed – past tense) 
The movie critic reviewed the film.  He gave it three stars.  The movie critic watched the film.  Then he shared his opinion.  He evaluated the movie.
He wrote a review. (In that sentence, review is a noun.)
To revise (verb) means to change or correct.
The publisher asked the author to revise the fourth chapter of her new novel.  The author has to change that chapter in some way: make it shorter, develop the plot (add to it), fix errors (correct).  
The author revised the chapter.  (past tense form of the verb)
Three weeks later, the author submitted her revisions.  (noun form of the word)
The publisher liked the revised chapter.  (used as an adjective meaning changed or corrected)
 
****  Depending on where you are, the word might mean
to study something already learned (to practice or prepare for evaluation).
Revise (UK)
Review (US)
The students reviewed the words they had to know for the test.  The students thought about those words again and studied them again.