In the first section of these lectures I outline the classical framework of the Hubble classification system. Because of space limitations I will focus on points of controversy concerning the physical interpretation of the Hubble sequence, showing how morphological ideas shape our understanding of galaxy evolution. I will then present an overview of the remarkable progress made in recent years in understanding how the local morphological composition has transformed into that seen the distant Universe, highlighting work from the Hubble Deep Field (HDF). Recent studies show quite clearly that the Hubble system does not provide a useful framework for describing the appearance of galaxies at redshifts z > 1.5. I argue that as a result of this work the Hubble system needs to be replaced by a system that is more objective, more physically meaningful, and which is applicable across a wider range of redshifts.