In this paper, the impact of limited resources on achievable rates in relay channels is investigated. Resource limitation is modeled as a rate constraint, Rbar, which constrains the rate at which a relay can reliably decode or source-code data. With this constraint in hand, the achievable rates for several protocols are derived and compared: decode-and-forward, estimate-and-forward, a Markovian amplify-and-forward and a hybrid scheme that combines decode-and-forward and amplify-and-forward. The key result is that the relative performance of these protocols in the unconstrained case is not maintained in rate constrained scenarios. The case of severe resource limitation (Rbar --> 0) is also considered. Previously established rates for unconstrained decode-and-forward and estimate-and-forward are re-examined in the context of optimal parameters and asymptotic performance. For most relay locations (topologies), either decode-and-forward and estimate-and-forward offers superior performance. However, for severe rate constraints, amplify-and-forward generally offers the best performance.