The Law of the Three Unities, requiring "unity" of "time, place, and subject," is the most well-known of all theatrical constraints. It was first employed by the Ancient Greeks and later became more fully embraced in France. Another example is the Japanese prohibition of female acting in 1625, then the prohibition of young male actors in 1657, that create "Onnagata" witch is the ground of japanese theatrical tradition. In the Elizabethan theatre of Shakespeare, a similar ban forbade all actresses from appearing on stage, at all; the parts of women were generally played by boys. The plot of Shakespeare in Love turns on this fact.
In cinema, the Dogme 95 films form a body of work produced under voluntary constraints that severely limit both the choice of subjects and the choice of techniques used to bring them to the screen.
Another culturally significant constraint occurred in France. In the late seventeenth century (1697 to be exact) Italian companies were prohibited from appearing in France, so native actors - strolling players going from fairground to fairground, market place to market place - took over the Italian plays and made the roles their own with great success
But this aroused the jealousy of the Comedie Française which decided to outlaw all spoken dialogue except in its own theatre. To overcome this, the travelling players divided their plays into soliloquies and performed nothing but monologues - which brought them even greater success than previously. One actor would say his lines, run off into the wings, while another appeared in order to reply. He would then go off in his turn, allowing the first one to come back and reply, and so on and so forth.
After this, the Comedie Française declared that they alone had the right to use speech on stage. Consequently the public theatre found its way round this by using song instead of speech - and this is how French Operetta came into being. But then the Academy of Music proclaimed that they alone should be given the right to sing!
So in the markets and fairgrounds the itinerant actors created a new theatrical form by holding up cue-cards (like sub-titles or karaoke) containing the words of the plays or songs, which the audience then acted or sang for them. This became even more successful, with crowds coming from all around to see how the actors had overcome such rigid censorship. The popularity of their shows rapidly increased, thereby creating a perfect example of theatrical constriction through anticipatory plagiarism for the Outrapo.
Some of the restrictions, or traditions born of them, may have still been in place in the nineteenth century, at least if Marcel Carné's Les Enfants du Paradis is a reliable guide. This also explains why France has given the world so many mimes.
Other theatrical constraints are also known as superstitions.