Nanoscale pores are ubiquitous in biological systems while artificial nanopores are being fabricated for an increasing number of applications. Biological pores are responsible for the transport of various ions and substrates between the different compartments of biological systems separated by membranes while artificial pores are aimed at emulating such transport properties. As an experimental method, electrophysiology has proven to be an important nano-analytical tool for the study of substrate transport through nanopores utilizing ion current measurements as a probe for the detection. Independent of the pore type, i.e., biological or synthetic, and objective of the study, i.e., to model cellular processes of ion transport or electrophysiological experiments, it has become increasingly important to understand the dynamics of ions in nanoscale confinements. To this end, numerical simulations have established themselves as an indispensable tool to decipher ion transport processes through biological as well as artificial nanopores. This article provides an overview of different theoretical and computational methods to study ion transport in general and to calculate ion conductance in particular. Potential new improvements in the existing methods and their applications are highlighted wherever applicable. Moreover, representative examples are given describing the ion transport through biological and synthetic nanopores as well as the high selectivity of ion channels. Special emphasis is placed on the usage of molecular dynamics simulations which already have demonstrated their potential to unravel ion transport properties at an atomic level.