Vacuum fluctuations distinguish quantum field theory from non-relativistic quantum mechanics. The phenomena that result from the modification of vacuum fluctuations by external fields or boundary conditions are known as Casimir effects. The study of Casimir effects has been plagued by divergences. In these lectures I describe the framework my collaborators and I have developed for the study of Casimir effects in the context of renormalizable quantum field theories, where divergences can be regulated, analyzed, and, for properly defined observables, removed. I discuss several examples: first a model in which quantum fluctuations stabilize a soliton, next, the physically important case of the Standard Model, where no quantum stabilized soliton has yet been discovered, and finally the ``classic'' Casimir effect.

PACS numbers: 11.10.--z, 11.27.+d