Abstract: The familiar Pauli spin matrices are both unitary and Hermitian and thus can be used in modelling both the evolution amd the measurement of two-level quantum systems. A generalization to unitary matrices in a d-dimensional context is motivated by a "Fourier" property of the Pauli matrices, and the resulting family has proved useful in problems in quantum information theory. In this talk we discuss the motivating definition, noting that the resulting matrices have appeared earlier in a variety of contexts. We illustrate their usefulness in two problems: the so-called separability problem and the problem of constructing mutually unbiased bases. Other problems in which the matrices are useful will be mentioned if time permits.