In this paper, a survey of reconfigurable computing is presented. There have been other surveys in this field, but none as exhaustive as this one tries to be. The main goal of this paper is to consider a large variety of different approaches to the field of reconfigurable computing, and to make a thorough classification. This classification is aimed at helping the understanding of the current systems, as well as the development of new systems. We first define the classification criteria and the classification itself. Each class is described briefly. Next, we classify the existing systems, based on their dominating characteristic, and finally we list each surveyed system under one of the classification classes. Each presented example is described using the same template (authors, essence of the approach, details of interest, advantages, drawbacks).