In Approximation Algorithms, we try to go as far as possible towards constructing an approximation. In Complexity Theory, people try to go as far as possible towards proving that a problem is not approximable.
There is a natural meeting point, at the limit of our respective searches -- the instances for which we have the greatest difficulty designing approximations are precisely the instances for which, on the other side of the barrier, people try to prove lower bounds. Ultimately, it is the same combinatorial structure that frustrates our attempted algorithms and that provides the ingredients of their lower bounds.
The researchers, like me, whose domain of specialty is algorithms, work on only one side of the barrier, but the ones whose particular strength, at the core, is in combinatorial structure, can work on both sides.