The aim of this paper is to make an overview on three generalizations to higher dimensions of the function's theory of a complex variable. The first one concerns the so-called monogenic functions which were introduced by F. Brackx, R. Delanghe and F. Sommen, the second is the theory of hyper-monogenic functions developed by H. Leutwiler, and the last one studies the theory of holomorphic Cliffordian functions due to G. Laville and I. Ramadanoff. The basic notions in this three theories will be given. Their links and differences will also be commented.