In this work, we investigate the transverse magnetoresistance of materials by combining the Fermi surfaces calculated from first principles with the Boltzmann transport theory approach relying on the semiclassical model and the relaxation time approximation. We first consider a series of simple model Fermi surfaces to provide a didactic introduction into the charge-carrier compensation and open-orbit mechanisms leading to nonsaturating magnetoresistance. We then address in detail magnetotransport in three representative materials: (i) copper, (ii) bismuth, and (iii) tungsten diphosphide. Furthermore, the calculations allow for a full interpretation of the observed features in terms of the Fermi surface topology. Our study thus establishes guidelines to clarifying the physical mechanisms underlying the magnetotransport properties in a broad range of materials.