Thermonuclear fusion of light atoms is the primary energy source of stars, such as our Sun, that led to the emergence of life on Earth. However, its economic exploitation as a virtually unlimited and clean energy source is yet to be developed. One of the most promising designs for a nuclear fusion reactor is the tokamak, a toroidal device that uses strong magnetic fields to contain matter so it may be heated to fusion-relevant temperatures of $\sim 10^8\;^\circ$C. A substantial fraction of the heating power, required to maintain fusion-relevant plasma conditions, is transported across magnetic flux surfaces and channeled through a thin region of open magnetic field lines that surround the confined zone, the scrape-off layer, towards the plasma wall interface at the divertor targets. If left unmitigated, anticipated target heat fluxes in current reactor designs exceed the material limit and raise the need for an accurate predictive model of heat transport and power dissipation in the plasma edge to achieve a viable reactor configuration. This doctoral thesis is devoted to further understanding of divertor power exhaust, a key challenge on the way towards fusion energy, and contributes to the validation of such a predictive model, the SOLPS-ITER code. This work employs stringent comparisons between simulation results and experiments on the TCV tokamak to validate this model, where possible, and/or indicate remaining problems. This thesis presents the first scrape-off layer simulations that fully account for drifts, currents, carbon impurities and kinetic neutrals, for the TCV tokamak, and thereby provides unprecedented insight into drift-driven transport and plasma-neutral interaction within its divertor. In an initial stage, the SOLPS-ITER code was used to predict the effectiveness of divertor gas baffles to guide the first baffled TCV campaign. The experimental assessment in 2019 confirmed the essential simulation predictions. Drift simulations identify the diamagnetic current as the dominant cross-field contribution to the divertor charge balance. The resulting characteristics of target current profiles are tested and confirmed in TCV measurements. It is demonstrated, for the first time, that such electric currents give rise to a potential well below the magnetic X-point for the unfavorable magnetic field direction for H-mode access in highly resistive, i.e. low temperature, divertors. The simulation result is supported by reduced analytic models that highlight the underlying physics. The prediction is tested and confirmed in TCV experiments following novel diagnostic capabilities. The presence of such a potential well is shown to substantially reshape the divertor transport in detached divertor conditions. The simulations identify the $E\times B$-drift as the dominant radial transport channel for particles, heat and momentum in the divertor. A stringent comparison of simulation results to a wide set of edge-relevant diagnostics yields typically excellent qualitative agreement, but quantitative differences remain: the simulations conclude a colder and denser divertor plasma state with an overestimated neutral pressure. The identified shortcomings in this approach will contribute to further development towards a predictive divertor model of present day, and future fusion devices.