I must admit solid fuel rockets don't interest me that much as their application for space rockets is somewhat limited and they seem to quickly go out of fashion.

Solid rocket fuel gives a lot of kick but not very good fuel efficiency. Thus they work reasonably well as boosters.

Big problem is that solid rocket engines are kind of like dumb tubes. You basically have no control. They have to be built specifically for a particular flight profile. With liquid fuel you can have electronic systems which can increase or decrease flow of propellant by adjusting the turbo pumps. You could even shut down the engines entirely.

I don't know much about this but I believe I have read that solid booster make a lot of sense for weapon systems as you can keep them ready to go for a long time.