Diffractive Higgs production

Instrumenting the LHC to measure the outgoing protons in the process pp -> p+X+p opens up new possibilities for physics studies in the Standard Model and beyond. In this talk I first present an overview of the underlying QCD calculation and its uncertainties. I then move on to present a variety of new physics scenarios which one would want to explore via this unique channel. There is a short discussion of the recent CDF data which may provide evidence for the existence of central exclusive jet production at the Tevatron.