Since Hubble's classification famous 1926 paper outlining his system, understanding galaxy morphology has been an important goal of extragalactic astronomy. For a long time, the subject was little more than descriptive because of a lack of basic data, but today morphology is very much more than a series of type codes and symbols. There is little doubt that morphology was a first logical step in approaching an understanding of galaxies. However, it is reasonable to ask where morphology has led us up to now. This is important to consider at a time when extragalactic astronomy is making great strides on both theoretical and observational fronts.
In this overview I will focus mainly on the fundamentals of morphological classification, both in theory and in practice. The subject is very broad and cannot cover all of the quantitative aspects which have been addressed in recent years. Nevertheless, an attempt is made to review advances in understanding specific types from research during the past 15 years.