Solid and liquid electrolytes for electrochemical energy storage and conversion cells, such as batteries, supercapacitors and fuel cells, contain often high concentrations of mobile ions. Therefore, the ion dynamics in these electrolytes is characterized by pronounced directional correlations between successive ion movements, which exert a strong influence on charge and mass transport. In this manuscript, we review the relevant transport properties of (i) single-ion conducting solid electrolytes and of (ii) liquid electrolytes with a single type of cations and a single type of anions. All transport quantities are based on Onsager's linear irreversible thermodynamics and are defined in the laboratory frame of reference, so that they can be easily related to correlations functions of the equilibrium ion dynamics by means of linear response theory. In the case of single-cation conducting solid electrolytes, we discuss how the complex interplay between cation-cation and cation-lattice interactions leads to a competition between cation self-correlations and distinct-cation correlations. In the case of liquid electrolytes, we describe how cation-cation, anion-anion, and cation-anions correlations influence the various transport quantities, such as total ionic conductivity, Haven ratio, salt diffusion coefficient and cation transference numbers. Moreover, we discuss how, in dilute liquid electrolytes, ion correlations can be governed by ion pair formation. Finally, the competition between cation/ anion and cation/polymer chain interactions can lead to negative cation transference numbers in polymer electrolytes, i. e. to cations migrating towards the positive electrode. Taken together, these case studies showcase how ion correlations in electrolyte systems can strongly influence the overall efficiency of energy storage and conversion devices due to transport limitations.[a] Dr.