<p>Understanding electronic transport in materials is essential to both fundamental and applied physics, as it directly influences critical properties such as the mobility of semiconductors and the efficiency of thermoelectric materials. Electron transport hinges on electronic structure of a material and various scattering events. Among these, scattering by phonons stands out as one of the most fundamental mechanisms, as it occurs even in pristine single crystals. But only recently have advances in the development of accurate first-principles methods allowed the precise calculation of electronic transport properties entirely from first principles, without relying on experimental parameters. This Technical Review presents the underlying physics of phonon-limited linear transport, primarily within the framework of the Boltzmann transport formalism but also for alternative approaches, such as the Landauer–Büttiker and Kubo frameworks. In addition, this Review covers technical aspects of implementing these formalisms, including their limitations and the scope of their applicability. Finally, we will discuss some specific transport regimes, such as transport in a strong electric field or involving the effect of spin–orbit coupling.</p>