Galaxy morphology is a product of how galaxies formed, how they interacted with their environment, how they were influenced by internal perturbations, AGN, and dark matter, and of their varied star formation histories. This article reviews the phenomenology of galaxy morphology and classification with a view to delineating as many types as possible and how they relate to physical interpretations. The old classification systems are refined, and new types introduced, as the explosion in available morphological data has modified our views on the structure and evolution of galaxies.