Non-thermal, leptonic radiation processes have been extensively studied for the interpretation of the observed radiation from jets of Active Galactic Nuclei (AGN). This work addresses the synchrotron and Inverse Compton scattering (ICS) mechanisms, and investigates the potential of a self-consistent, time-dependent approach to currently unsolved problems. Furthermore, it examines how deviations from standard, one-zone models can modify the radiated spectrum. A detailed analysis of the shape of the ICS spectrum is also performed. In the first part a possible interpretation of the hard γ-ray blazar spectra in the framework of leptonic models is investigated. It is demonstrated that hard γ-ray spectra can be generated and maintained in the presence of energy losses, under the basic assumption of a narrow electron energy distribution (EED). Broader spectra can also be modeled if multiple zones contribute to the emission. In such a scheme, hard flaring events, like the one in Mkn 501 in 2009, can be successfully interpreted within a "leading blob" scenario, when one or few zones of emission become dominant. In the second part the shape of the Compton spectrum close to the maximum cutoff is investigated. Analytical approximations for the spectral shape in the cutoff region are derived for various soft photon fields, providing a direct link between the parent EED and the upscattered spectrum. Additionally, a generalization of the beaming pattern for various processes is derived, which accounts for non-stationary, anisotropic and non-homogeneous EEDs. It is shown that anisotropic EEDs may lead to radiated spectra substantially different from the isotropic case. Finally, a self-consistent, non-homogeneous model describing the synchrotron emission from stratified jets is developed. It is found that transverse jet stratification leads to characteristic features in the emitted spectrum different to expectations in homogeneous models.