The storage medium for CSP is typically some kind of molten salt mixture (NaNO3, KNO3, Ca(NO3)2) which is then used on a closed circuit of water to power steam turbines. Right now this is limited to large facilities. In practice, CSP can be done on a small modular scale.
Here's an example of CSP at a large scale in Spain: https://www.youtube.com/watch?v=LMWIgwvbrcM There are also other places in world where facilities like these exist.
Here's an example of CSP at a smaller scale: https://www.youtube.com/watch?v=-SsJBobMpAk However, they use glycol (smaller thermal capacity) as a heat transfer medium instead of molten salt.
As for batteries for devices, that wouldn't necessarily equate to a golden age of solar energy because there is still larger issue of how the energy will get to the device and at what cost.