Coarse-to-fine approaches use sequences of increasingly fine approximations to control the complexity of inference and learning. These techniques are often used in NLP and vision applications. However, no coarse-to-fine inference or learning methods have been developed for general first-order probabilistic domains, where the potential gains are even higher. We present our Coarse-to-Fine Probabilistic Inference (CFPI) framework for general coarse-to-fine inference for first-order probabilistic models, which leverages a given or induced type hierarchy over objects in the domain. Starting by considering the inference problem at the coarsest type level, our approach performs inference at successively finer grains, pruning high- and low-probability atoms before refining. CFPI can be applied with any probabilistic inference method and can be used in both propositional and relational domains. CFPI provides theoretical guarantees on the errors incurred, and these guarantees can be tightened when CFPI is applied to specific inference algorithms. We also show how to learn parameters in a coarse-to-fine manner to maximize the efficiency of CFPI. We evaluate CFPI with the lifted belief propagation algorithm on social network link prediction and biomolecular event prediction tasks. These experiments show CFPI can greatly speed up inference without sacrificing accuracy.