Electrochemical energy storage is one of the few options to store the energy from intermittent renewable energy sources like wind and solar. Redox flow batteries (RFBs) are such an energy storage system, which has favourable features over other battery technology, e.g. solid state batteries, due to their inherent safety and the independent scaling of energy and power content. However, because of their low energy-density, low power-density and the cost of components such as redox species and membranes, commercialised RFB systems like the all-vanadium chemistry cannot make full use of the inherent advantages over other systems. In principle, there are three pathways to improve RFBs and to make them viable for large scale application: First, to employ electrolytes with higher energy density. This goal can be achieved by increasing the concentration of redox species, employing redox species that store more than one electron or by increasing the cell voltage. Second, to enhance the power output of the battery cells by using high kinetic redox species, increasing the cell voltage, implementing novel cell designs or membranes with lower resistance. The first two means reduce the electrode surface area needed to supply a certain power output, thereby bringing down costs for expensive components such as membranes. Third, to reduce the costs of single or multiple components such as redox species or membranes. To achieve these objectives it is necessary to develop new battery chemistries and cell configurations. In this review we focus on a comparison of promising cell chemistries, be they all-liquid, slurries or hybrids combining liquid, gas and solid phases.Aim is to elucidate which redox-system is most favourable in terms of energy-density, power-density and capital cost. Also the choice of solvent and the selection of an inorganic or organic redox couples with the entailing consequences are discussed.