Multiplex networks offer an important tool for the study of complex systems and extending techniques originally designed for single--layer networks is an important area of study. One of the most important methods for analyzing networks is clustering the nodes into communities that represent common connectivity patterns. In this paper we extend spectral clustering to multiplex structures and discuss some of the difficulties that arise in attempting to define a natural generalization. In order to analyze our approach, we describe three simple, synthetic multiplex networks and compare the performance of different multiplex models. Our results suggest that a dynamically motivated model is more successful than a structurally motivated model in discovering the appropriate communities.