**Robert Biele 1,\*,† and Roberto D'Agosta 2,3,\*,†**


### Received: 5 July 2019; Accepted: 29 July 2019; Published: 2 August 2019

**Abstract:** Almost any interaction between two physical entities can be described through the transfer of either charge, spin, momentum, or energy. Therefore, any theory able to describe these transport phenomena can shed light on a variety of physical, chemical, and biological effects, enriching our understanding of complex, ye<sup>t</sup> fundamental, natural processes, e.g., catalysis or photosynthesis. In this review, we will discuss the standard workhorses for transport in nanoscale devices, namely Boltzmann's equation and Landauer's approach. We will emphasize their strengths, but also analyze their limits, proposing theories and models useful to go beyond the state of the art in the investigation of transport in nanoscale devices.

**Keywords:** electronic transport; thermal transport; strongly correlated systems; Landauer-Büttiker formalism; Boltzmann transport equation; time-dependent density functional theory; electron–phonon coupling
