In this paper, the main achievements and problems of the application of all-atom molecular simulations, with particular attention for Molecular Dynamics (MD), will be critically reviewed. Starting from unfolding simulations, through biased simulations, which require a knowledge of the native state conformation, to folding studies based on the simple knowledge of the protein (or peptide) sequence, the strengths and weaknesses of theoretical approaches to the study of folding and their matching with experimental observations will be discussed. Finally, we will give a critical outlook on the possible developments of this field in the near future.