Do sprint reviews have to be during the current sprint?

How are you finding time for the Sprint Retrospective, which also requires the whole Scrum Team and is the last thing to happen in a Sprint?

Yes, the Sprint Review is the last event of the Sprint:

The Sprint is a container for all other events.

and

The Sprint Review is the second to last event of the Sprint...

Following your Sprint Review, you would also hold a Sprint Retrospective, which "concludes the Sprint". The new Sprint would begin with Sprint Planning, which "initiates the Sprint by laying out the work to be performed for the Sprint". There would be minimal working hours between the Sprint Retrospective and Sprint Planning.

My recommendation tends to be that teams avoid Scrum events on Mondays and Fridays. Although you've found one problem with scheduling the events with people who share limited overlap in working hours, there are others. In the United States, and perhaps other countries as well, many holidays fall on Mondays and Fridays, where employees have a company-mandated day off. Mondays and Fridays are also prime days for individuals to take off to have long weekends. Aligning the Scrum events on Tuesdays, Wednesdays, and Thursdays tends to yield better participation and fewer conflicts.

I'd agree with Thomas. I always suggest not having Sprints end on a friday for exactly this reason. Why not move things around so sprint ends on a tuesday or wenesday? 



As for the specific answer to your question though, yes a Sprint review has to be in the current sprint. 



You can't start a new Sprint without sprint planning, and sprint planning before you have a sprint review negates the inspect and adapt opportunity , and prevents us changing the product backlog based on feedback. 



It will quickly become a fixed plan being delivered incrementally, which is not Scrum.

I'm going to join in on the "don't have sprints end/start on Friday or Monday".  

I had a similar situation that you have.  What the team decided to do was to end a day with the Sprint Review and Sprint Retrospective.  The next day would start with Sprint Planning. This was not ideal because it could mean that some people go a day with nothing to do that is related to a sprint but it was the best that the team could agree upon.

I had another team agree to meet at a time that would result in the least amount of lost time for all people in the team.  Both teams worked a modified schedule for the end/beginning of the Sprint.  The team was split between the United States and India. They shifted so that everyone could be available at the same time to have the events run one after another.  This was a bit tricky because it resulted in early morning (as in hours before the sun comes up) for part of the team and late at night (as in after the sun goes down) for the other part.  It was also a bit tricky to get the stakeholders involved but since the Review was the first of the events it could be done.  The stakeholders understood the reason for their involvement and were willing to be available. The rest of the Sprint, the team worked their "normal" hours. 

Whenever you have a team this distributed by even a few hours, the team has to make concessions.  When that time difference is large, it becomes even more important to be flexible.