To uniformize a binary relation means to find a partial function whose graph lies in the relation and whose domain coincides with that of the relation. Said differently it consists of selecting a unique image for each element of the domain. Depending on the class of relations, it is possible or not to uniformize the relations by functions in the same class.

I will not give a survey, rather talk of what I know of the topic, which is mainly binary rational relations over finite and infinite words and some connected problems.