A systematic description of microscopic mechanisms is necessary to understand mass transport in solid and liquid electrolytes. From Molecular Dynamics (MD) simulations, transport properties can be computed and provide a detailed view of the molecular and ionic motions. In this work, ionic conductivity and transport numbers in electrolyte systems are computed from equilibrium and nonequilibrium MD simulations. Results from the two methods are compared with experimental results, and we discuss the significance of the frame of reference when determining and comparing transport numbers. Two ways of computing ionic conductivity from equilibrium simulations are presented: the Nernst-Einstein approximation or the Onsager coefficients. The Onsager coefficients take ionic correlations into account and are found to be more suitable for concentrated electrolytes. Main features and differences between equilibrium and nonequilibrium simulations are discussed, and some potential anomalies and critical pitfalls of using nonequilibrium molecular dynamics to determine transport properties are highlighted.