Over the years, research on the anaerobic digestion of solid waste has mainly focused on single feedstocks with a fixed composition. Nevertheless, the impact assessment that drastic changes in the type and composition of feedstock might have on AD process stability has not been investigated in depth. The existence of a wide variety of organic solid waste whose generation and composition are highly dependent on seasonality, just as the possibility of using treatment plant facilities already in operation for treating new waste, makes it necessary to improve our knowledge of transitory states in AD. This chapter aims to provide insight into research on transitory states during the AD process when the type or composition of the feedstock has suffered a change to assess whether the AD process was finally able to adapt to system disturbances. Information about process stability control and microbial population adaptation, among others, derived from the transition states will be addressed.