This chapter focuses on two specific mechanisms: afterslip and the rate-dependent reduction in the fault friction. It reviews the main assumptions and analytical steps proposed to explain the temporal behavior of aftershocks, in terms of both a time-dependent friction and afterslip dynamics. The chapter presents how two approaches can be combined. More precisely, it re-derives the evolution of a single block, when a stress drop is applied, both in the presence of a velocity-weakening rate-and-state friction law and in the presence of a velocity-strengthening friction law. The approach of a model composed of two spring slider systems is combined with different frictions with the further ingredient of friction heterogeneity. The chapter also presents the analytical derivation of the Omori law according to the interpretation proposed by Dieterich.