Bubbles in electrolysis exhibit significant complexities that greatly affect mass transport at gas-evolving electrodes. This renders disentangling the relevant effects through experiments an extremely tedious task. Therefore, in this thesis we utilize numerical simulations to unravel the controlling mechanisms of mass transfer at gas-evolving electrodes. In chapter 1, we combine the in-situ experiments with numerical simulations to study the effect of single-phase natural convection on the growth and dissolution of bubbles adhering to the electrode. Untangling the effect of diffusion and natural convection, we observe that the experimentally measured bubble evolution can only be accurately described once the flow induced by buoyancy forces is taken into account in addition to the diffusive transport. Furthermore, we reveal the effect of design parameters such as bubble spacing and their arrangement in a clustered network on the convective pattern and the resultant bubble dynamics. In chapter 2, we investigate micro- and macro-convection caused by bubble growth and rise in the electrolyte solution. First, we quantify the hydrogen and electrolyte transport at the electrode by defining an effective Grashof number which accounts for buoyancy forces of gas-in-liquid dispersion. Our findings highlights the dominance of two-phase buoyancy-driven convection over other mass transfer mechanisms. Next, we quantify hydrogen transport to the bubble and derive an expression for gas-evolution efficiency, which is key in determining the bubbles evolution and hence the following mass transfer processes in such systems. In chapter 3, we look into the downward dissolution dynamics of carbon dioxide in a cylindrical water barrier employing experiments and simulations. We reveal that convection causes front convolutions and steepens the gradients nearby. This leads to enhanced diffusive flux across the interface and hence faster propagation of the front. Our findings offer broader insight into the secure storage of CO2 in carbon capture and storage technologies.