Checking properties like if a point is inside is based on checking the same property on the elementary solids. Construction of mechanical parts including filets or shells is very complex. In some extends CSG inspired the parametric systems available today which mix the history tree and the Brep representation. But parametric systems are far more powerful because they include local operations like filleting. In the Brep approach solids are defined and stored by their boundary.
Every boolean operation leads to a complex computation.
It has been a long challenge for Solid modeling kernel developers to have reliable algorithms for this computation. The mathematical fundaments of BRep is the theory of 3D manifolds. It includes notion like differential topology. Almost all commercial CAD systems support BRep modelers. Facettized versus Exact.