PACS 81.07.-b, 81.15.HiWe give a bird's-eye view of the interface formation during MBE growth of various quasi lattice-matched as well as highly-mismatched semiconductor heterostructures. We show that the parameters controlling the growth mode and the interface formation are numerous and that the optimum interface configuration depends on the materials system and on the target application. Our results obtained from various semiconductor materials systems demonstrate that this growth and interface-related problem is much more complex than it has often been considered for many years.