The quantitative description of electrical and magnetotransport properties of solid-state materials has been a remarkable challenge in materials science over recent decades. Recently, the discovery of a novel class of materials—the topological semimetals—has led to a growing interest in the full understanding of their magnetotransport properties. In this review, the strong interplay among topology, band structure, and carrier mobility in recently discovered high carrier mobility topological semimetals is discussed and their effect on their magnetotransport properties is outlined. Their large magnetoresistance effect, especially in the Hall transverse configuration, and a new version of a three-dimensional quantum Hall effect observed in high-mobility Weyl and Dirac semimetals are reviewed. The possibility of designing novel quantum sensors and devices based on solid-state semimetals is also examined.