  In the 1930s Tarski showed that real quantifier elimination was possible, and
in 1975 Collins gave a remotely practicable method, albeit with
doubly-exponential complexity, which was later shown to be inherent. We discuss
some of the recent major advances in Collins method: such as an alternative
approach based on passing via the complexes, and advances which come closer to
"solving the question asked" rather than "solving all problems to do with these
polynomials".
