Latent heat - Ice
Heat engines need temperature difference so it doesn't matter whether we store heat, or cold.
Before refrigeration ice houses were built to hold ice during summer. The one pictured here at Cedar Falls USA, held up to 800 tons of ice.
It takes 334 kJ/kG to melt ice. (80 cal/g).
The scientific term for the energy needed for melting is "enthalpy of fusion" . Wiki
Latent heat - Steam
Steam carries and stores a tremendous amount of energy and has always been used for this in industry.
It is limited by heat losses and pressure limits of equipment.
It takes 2,260 KJ/KG to vaporise water. This varies a little with temperature and pressure.
Latent heat - Liquid air
Air can be liquefied at night when the air is cool and power is cheap. It is cooled to -190oC and held in a giant vacuum flask until it is needed. Then the liquid is heated, preferably with waste heat and vaporised, driving a turbine to produce electricity.
In the liquid form it occupies one thousandth the volume of the air.
The process is 25-70% efficient depending on whether the heat for vaporisation is counted. Low grade waste heat can be used, so it would be useful for power stations.
Highview Power Storage claims an AC to AC round-trip efficiency of 70%, by using an otherwise waste heat source at 115°C.
Phase change air conditioning
Changing from solid to liquid, or liquid to vapour, is called a phase change.
Energy for air conditioners can be saved by freezing water over night when the air is cool and electricity is cheap. Then during the day air can be pushed over the ice to supply cool air. Modern phase change air conditioners used different substances for better efficiencies.
Latent heat melting silicon
Latent Heat Storage is entering the market with a patented system originally developed by the CSIRO.
The high latent heat capacity and melting temperature of silicon make it ideal for the storage of large amounts of energy.
It runs at a significantly higher temperature than other thermal storage medium, and has a very large energy density. The stored thermal energy is recovered and converted back to electricity via a turbine or heat engine.