Solid state hydrogen storage is essentially a sponge made from a metallic hydride (NaAlH4, MgH2, LaNi5H6, etc) or some other material which either absorbs or releases hydrogen depending on its temperature.

Advantages: low pressure operation (reduced losses during extended storage), controllable and predictable release rates, much less risk of explosion vs pressurized hydrogen.

Disadvantages: larger, more expensive, and more than 10x heavier than a compressed liquid hydrogen container of equivalent capacity, plus chemical degredation over time can limit the lifetime charge/discharge cycle count of certain mediums.

Likely a metal hydride based system. It is at present the only geniuinely mature way of storing hydrogen in a solid state form.