We investigate the representations and the structure of Hecke algebras
associated to certain finite complex reflection groups. We first describe
computational methods for the construction of irreducible representations of
these algebras, including a generalization of the concept of $W$-graph to the
situation of complex reflection groups. We then use these techniques to find
models for all irreducible representations in the case of complex reflection
groups of dimension at most three. Using these models we are able to verify
some important conjectures on the structure of Hecke algebras.