Constrained writing is a literary technique in which the writer is bound by some condition that forbids certain things or imposes a pattern.
Constraints are very common in poetry, which often requires the writer to use a particular verse form.
The most common constrained forms of writing are strict restrictions in vocabulary, e.g. Basic English, E-Prime, defining vocabulary for dictionaries, and other limited vocabularies for teaching English as a Second Language or to children. This is not generally what is meant by 'constrained writing' in the literary sense, which is motivated by more aesthetic concerns. For example:
The Oulipo group is a gathering of writers who use such techniques.
The Outrapo group use theatrical constraints.
Gadsby is an English-language novel consisting of 50,100 words, none of which contain the letter "e".
In 1969, France's Georges Perec published La Disparition , a novel that did not include the letter "e". It was translated into English in 1995 by Gilbert Adair as "A Void".
In 2004, a new marvel from France: a novel, entirely without verbs: Le Train de Nulle Part ("The Train from Nowhere") by Michel Thaler . 
One famous constrained writing in the Chinese language is the Lion-Eating Poet in the Stone Den which consists of 92 characters, all with the sound shi.