A quark model is applied to the spectrum of baryons containing heavy quarks. The model gives masses for the known heavy baryons that are in agreement with experiment, but for the doubly-charmed baryon Ξcc, the model prediction is too heavy. Mixing between the ΞQ and Ξ′Q states is examined and is found to be small for the lowest lying states. In contrast with this, mixing between the Ξbc and Ξ′bc states is found to be large, and the implication of this mixing for properties of these states is briefly discussed. We also examine heavy-quark spin-symmetry multiplets, and find that many states in the model can be placed in such multiplets. We compare our predictions with those of a number of other authors.