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The Communications of the ACM article "The Silent (R)evolution of SAT" [1] gives an overview of some of the techniques used in SAT solvers. I believe it was posted on HN fairly recently.

[1] https://cacm.acm.org/magazines/2023/6/273222-the-silent-revo...

From what I learned from covering this in my Master's degree, the efficiency comes from the DPLL algorithm, which can efficiently solve many real world inputs, but still takes exponential time in the worst case.

I’d recommend reading about DPLL and CDCL. These are relatively simple concepts that you can code up yourself

Google or YouTube could probably give you a good nutshell answer to that.