Metal nanoparticles contain the active sites in heterogeneous catalysts, which are important for many industrial applications including the production of clean fuels, chemicals and pharmaceuticals, and the cleanup of exhaust from automobiles and stationary power plants. Sintering, or thermal deactivation, is an important mechanism for the loss of catalyst activity. This is especially true for high temperature catalytic processes, such as steam reforming, automotive exhaust treatment, or catalytic combustion. With dwindling supplies of precious metals and increasing demand, fundamental understanding of catalyst sintering is very important for achieving clean energy and a clean environment, and for efficient chemical conversion processes with atom selectivity. Scientists have proposed two mechanisms for sintering of nanoparticles: particle migration and coalescence (PMC) and Ostwald ripening (OR). PMC involves the mobility of particles in a Brownian-like motion on the support surface, with subsequent coalescence leading to nanoparticle growth. In contrast, OR involves the migration of adatoms or mobile molecular species, driven by differences in free energy and local adatom concentrations on the support surface. In this Account, we divide the process of sintering into three phases. Phase I involves rapid loss in catalyst activity (or surface area), phase II is where sintering slows down, and phase III is where the catalyst may reach a stable performance. Much of the previous work is based on inferences from catalysts that were observed before and after long term treatments. While the general phenomena can be captured correctly, the mechanisms cannot be determined. Advancements in the techniques of in situ TEM allow us to observe catalysts at elevated temperatures under working conditions. We review recent evidence obtained via in situ methods to determine the relative importance of PMC and OR in each of these phases of catalyst sintering. The evidence suggests that, in phase I, OR is responsible for the rapid loss of activity that occurs when particles are very small. Surprisingly, very little PMC is observed in this phase. Instead, the rapid loss of activity is caused by the disappearance of the smallest particles. These findings are in good agreement with representative atomistic simulations of sintering. In phase II, sintering slows down since the smallest particles have disappeared. We now see a combination of PMC and OR, but do not fully understand the relative contribution of each of these processes to the overall rates of sintering. In phase III, the particles have grown large and other parasitic phenomena, such as support restructuring, can become important, especially at high temperatures. Examining the evolution of particle size and surface area with time, we do not see a stable or equilibrium state, especially for catalysts operating at elevated temperatures. In conclusion, the recent literature, especially on in situ studies, shows that OR is the dominant process causing the growth of nanoparticle size. Consequently, this leads to the loss of surface area and activity. While particle migration could be controlled through suitable structuring of catalyst supports, it is more difficult to control the mobility of atomically dispersed species. These insights into the mechanisms of sintering could help to develop sinter-resistant catalysts, with the ultimate goal of designing catalysts that are self-healing.