Generally, London theatres are divided into West End, Fringe - some fringe are also known as Off West End - and repertory like The National Theatre (NT) and Shakespeare's Globe.
West End theatres are mainly concentrated in the 'West End' of London around Leicester Square, Strand and Shaftesbury Ave. They are commercial, mainly putting on large, expensive productions. Ticket prices can be high, sometimes as much as £70 (or £100 for so called premium seats), even more if buying from an agency. However, the cheapest tickets can be as low as £15 depending on the day of the week (although they may not be great views!)
Some West End theatres are not located in the West End. A couple are in Victoria, but are classed as West End because of their size and investment. The seating capacities can range from around 250 to over 2,000.
NT and GLOBE THEATRE
The National Theatre (NT) and the Shakespeare Globe Theatre are two of the most popular repertory companys in London. (Generally repertory theatre in London is when a selection of shows are rotated every few days so you can see several shows in one week at the same venue, some with the same cast)
The National Theatre (NT) is subsidised, which means it can take a risk with new and unknown writers, and plays that may not appeal to a wide audience. Having said that, probably the best plays are performed here. The very successful productions can transfer to the West End for a commercial run.
The Royal National complex houses three theatres, the Olivier, the Lyttelton and the Cottesloe, and as most performances are in repertory, you can see many plays in one week. The Shakespeare Globe Theatre season runs from April to September, and of course it mainly performs Shakespearean plays.
THE FRINGE/OFF WEST END/OTHER
Smaller theatres, including many pub theatres, are called Fringe, although some of these small theatres are also called Off West End, particularly those located in the West End of London, where most of the big commercial theatres are. These small theatres can vary in size, with seating capacities of around 40 to 400.
You can see some superb plays in these small theatres, and prices are much lower than those in the West End. The size of Fringe theatres brings you very close to the action and can provide a more intimate experience than the big West End theatres.
There are also some commercial theatres in London that are not West End or Fringe, like the Richmond and Wimbledon theatres, which are generally classed as regional. These theatres are mainly receiving houses for touring shows, which play for only a week or two.