Financial crises usually have severe consequences on the global economy and an intriguing question is whether structural breaks in the credit market can be modeled and monitored. Choosing firms' credit rating transition dynamics as a proxy of the credit market, we approach the problem in two steps. The first step is to model credit rating transitions as a piecewise homogeneous Markov chain with unobserved structural breaks and develop an inference procedure, and the second step is to discuss how statistical process control rules can be used to surveil structural breaks in firms' rating transition dynamics. Several surveillance rules, such as the LR/GLR rules, the extended Shiryaev's detection rule, and a Bayesian detection rule for piecewise homogeneous Markovian models. The effectiveness of these rules was analyzed via Monte Carlo simulations. We also provide a real example that used the surveillance rules to analyze and detect structural breaks in the monthly credit rating migration of US firms from January 1986 to February 2017.