The article is an overview study of research on accceleration as one of the basic methods applied in education of gifted pupils. In a present article, its basic types – namely content-based and grade-based acceleration, are specified at the beginning and some examples are mentioned. In the following sections, several important studies from abroad are presented which deal especially with effects of acceleration on academic outcomes and on important emotional and social aspects. In the end the article deals with criteria that should be used while deciding whether to accelerate or not a particular child.