The theory of Bernstein's algebras is revisited. Many results concerning the structure of Bernstein algebras (ideals, nilpotency and so on) are stated. For Bernstein-Jordan algebras, we give a definitive formulation of the theorem which characterizes them. Finally, we emphasize the importance of the invariant L (this ideal doesn't depend on the Peirce decomposition of the algebra) in the study of the structure of Bernstein's algebras.