Most if not all power used is generated almost instantly as needed. So when you look at solar (which is a great renewable) you run into the fact that it only generates power while the sun is out, and a specific amount of power.
This causes the problem of, how do you generate power at night and what do you do on rainy days or if a cloud covers the panels. You can substitute this with other renewable energy sources: wind, hydro, and nuclear, but wind has similar issues as solar and hydro and nuclear have huge upfront costs and take years to build.
So this is where coal and natural gas come in. Coal has the downside of being really bad for the environment but can start up within 10ish minutes of being needed. Gas is better for emissions (not great), but takes more time to startup.
A lot of companies use a mix of things along with buying and selling power with other companies (similar to a stock market). There are thoughts of trying to store power or looking at small scale nuclear plants.
Solar chart through the day:
Power use throughout the day:
Source: I work for a large power company
Ya! And there is a lot of research and investment into them. The problem is they lose capacity over time from being powered and drained (think phone batteries and other lithium batteries).
From what I know hydro batteries are actually really big with power companies. Basically pumping a bunch of water uphill when you have excess power, then using the reservoir like a hydro plant when you need power. They are really inefficient, but work surprisingly well at storing a lot of power