The paper studies the nature of “understanding” in condensed matter physics (CMP), mediated by the successful employment of its models. I first consider two obvious candidates for the criteria of model-based understanding, Van Fraassen's sense of “empirical adequacy” and Hacking's “instrumental utility”, and conclude that both are unsatisfactory. Inspired by Hasok Chang's recent proposal to reformulate realism as the pursuit of ontological plausibility in our system of knowledge, we may require the model under consideration to be understood (or intelligible) before claiming model-based understanding. Here the understanding of a model typically consists of the following: figuring out at least one plausible (preferably realistic) physical mechanism for the model, determining the theoretical consequences of the model by mathematically “probing” it and developing our physical intuitions about the model. I consider the q-state Potts model to illustrate. After having understood a model, we may employ the model to understand its target phenomena in the world. This is done by “matching” one of the interpretative models of the model with the central features of the phenomena. The matching should be motivated (ideally both theoretically and empirically) in the sense that we have good reason to believe that the central features of the phenomena can be thought of as having more or less the same structure as postulated by the interpretative model. In conclusion, I propose a two-stage account of model-based understanding in CMP: (1) understanding of a model and (2) matching a target phenomenon with a well-motivated interpretative model of the model. Empirical success and instrumental utility both play their roles in the evaluation of how successful the model is, but are not the essential part of model-based understanding.