In this paper, we review, analyze and compare representations for simplicial complexes. We classify such representations, based on the dimension of the complexes they can encode, into dimension-independent structures, and data structures for three- and for two-dimensional simplicial complexes. We further classify the data structures in each group according to the basic kinds of the topological entities they represent. We present a description of each data structure in terms of the entities and topological relations encoded, and we evaluate it based on its expressive power, on its storage cost and on the efficiency in supporting navigation inside the complex, i.e., in retrieving topological relations not explicitly encoded. We compare the various data structures inside each category based on the above features.