The formation of late-type galaxies is one of the open questions of cosmology, from both the observational and the theoretical point of view. Furthermore, the observations show the existence in the local Universe of peculiar late-type galaxies (e.g. ring galaxies and giant low surface brightness galaxies), which cannot be modeled with current cosmological simulations. Similarly, even non-peculiar disc galaxies show features which are hard to explain, such as lopsidedness. This talk will discuss the state- of-art of the formation and evolution of peculiar and lopsided disc galaxies.