AbstractWe discuss recent results of hydrodynamical simulations of galaxy formation in a Λ Cold Dark Matter universe, focusing on galaxies of similar mass to the Milky Way, and with a variety of formation and merger histories. We investigate the present‐day properties of disks and spheroids, in terms of stellar ages, spatial structure and dynamics; as well as the evolution of the disks. We find that disks are young, and usually composed of two or more components: the youngest stars define thinner disks that rotate ∼2 times faster than thicker disks. The latter are populated by older stars, and have 2–3 times larger velocity dispersions than the younger population. Spheroids are old and are very diverse; their inner regions are sometimes characterized by the presence of prominent bars. The disks evolve significantly during evolution. In particular, we find that major mergers and misaligned gas accretion are able to completely or partially destroy disks. These results suggest that the survival probability of disks, and therefore the final morphology of galaxies, strongly depends on the particular formation and merger history of their parent haloes. Our results show that galaxy diversity arises naturally in ΛCDM as a result of the different evolutionary paths of dark matter haloes. We also discuss the most important open problems in this field (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)