Renewables, particularly solar, seem to offer our clearest option for a long-term source of energy large enough to support civilization. A power grid supported primarily by solar would produce far more energy during the day than at night. Some types of power production can be brought online during the night (such as hydroelectric), but these are far from enough to support the needs of the grid.
If you have too much energy in the day and not enough at night, storing it is the natural thought. Unfortunately, the amount of energy required to keep things online during the night is huge. There are several different technologies (and some commercial projects) which seem to have potential.
How much storage do we need?
Depends on what proportion of the grid runs on solar, how much heavy industry and transport respond to pricing by operating plants only when electricity is cheap, how seasonal solar power is, how far we can efficiently redistribute power, and how tolerant of power outages we can make society (with redirection to critical infrastructure support and home batteries).
Woefully incomplete guesstimate model.
Differential pricing
Differential pricing is a tool to give good incentives. If electricity is cheap in the day and expensive at night as well as freely tradable, there is strong economic reason for technology development and infrastructure investment.
Which technologies seem promising?
WIP, waiting on table tag