The topic of the thesis is medium access which is one of the fundamental problems in wireless networks: as a result of the spatial nature of wireless signals wireless transmissions experience interference from each other, thus making spatially close simultaneous transmissions conflict with each other. A naturally arising problem in this context is the problem of scheduling where the transmission requests must be organized into a small number of subgroups each of which can transmit simultaneously in one time slot, the ultimate goal being executing all transmission in the minimum time. The thesis considers scheduling problems and related problems in the well known SINR (signal-to-interference-and-noise-ratio) model and extends the current state of the art on the treatment of these problems from a theoretical point of view. Several complexity results and approximation algorithms are presented for the aforementioned problems. A graph-based framework is introduced which is used to obtain results for medium access problems in the SINR model, as well as to extend the idealistic geometric SINR model towards more realistic depiction of real-world networks.