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Aftershocks provide a wealth of information that can be used to better understand the physics of earthquake processes. The occurrence of aftershocks is an outcome of complex dynamics in the brittle part of the Earth's crust initiated by a main shock. This dynamics is a combined effect of different processes taking place in a highly heterogeneous media over a wide range of temporal and spatial scales. In this presentation aftershock sequences in California are studied in order to better understand their scaling properties. In the temporal domain, the decay of aftershock rates can be described by the generalized Omori's law, which incorporates three empirical laws: the Gutenberg-Richter relation for frequency-magnitude scaling, the modified Omori's law for the temporal decay of aftershocks, and the modified Bath's law for the difference between the magnitudes of a main shock and its largest aftershock. The analysis of decay rates suggests that the parameter c in the generalized Omori's law is not a constant but scales with the lower magnitude cutoff and plays the role of a characteristic time in the establishment of Gutenberg-Richter scaling. Distributions of interoccurrence times between earthquakes in aftershock sequences are also analyzed and a model based on a non-homogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of interoccurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis. It is argued that the NHP process combined with the generalized Omori's law can be used to a good approximation to quantify the observed temporal scaling of interoccurrence times between earthquakes in aftershock sequences. The validity of these scaling laws is evidence that earthquakes exhibit self-organization and complexity.