The evolutionary space of a single enzyme is far too large to explore systematically. Despite this, there has been much success in the field of in vitro evolution, both from enzymes with starting activity and from random sequence. What can we say about the structure of evolutionary space based on these findings? What can we say about optimal methods for the discovery and improvement of enzymes? Drawing on recent experimental and theoretical work we will go over several ways by which this problem has been approached in the past and will explore questions of how to describe the immense space of possible enzymes in a systematic way.