Batteries where the energy is stored within the cell (the sort you might have in your torch, camera, phone or laptop, and ordinary car batteries) are generally far more expensive, in proportion to their energy capacity, than any of the other methods of energy storage discussed here – too expensive to use for grid storage (other than short term, to meet peaks). Flow batteries, where the energy is stored in liquids in tanks and passed through the cell during charging and discharging, are cheaper – but still probably not competitive with the other technologies for long term storage.
Fuel storage, on the other hand, is very cheap – with the exception of the storage of hydrogen. Hydrogen can be stored in huge containers at modest pressures, or smaller containers either at very high pressures, or as liquid at very low temperatures. Any of these options are expensive if you’re storing large quantities of energy. (There is another possible method, if you have a deep lake or deep sea handy, using the same technology discussed in Underwater Compressed Air Engineering. There are also methods where the hydrogen is absorbed into the crystal lattice of solids, but these are much more expensive.)
This is unfortunate, as hydrogen is the easiest fuel to produce using electricity, when electricity supply exceeds demand. However, it is possible to produce other fuels, notably methane (“natural” gas).
Methane can be produced using the Sabatier reaction, in which carbon dioxide (possibly a by-product of liquid air energy storage) and hydrogen (produced by electrolysis of water) react at 300° to 400°C, in the presence of a catalyst, to produce methane and water. Methane is a convenient medium for energy storage, and a convenient medium for delivery of energy for various puposes such as heating, combined heat and power, or electricity generation – especially given the fact that massively extensive facilities for this already exist.