Proton-(anti)proton collisions at the LHC or Tevatron typically involve experimental restrictions on the hadronic final state and generic parton momentum fractions. In this situation, factorization at the scale of the hard interaction does not yield standard parton distribution functions (PDFs) for the initial state. The measurement restricting the hadronic final state probes the proton prior to the hard collision and the hard collision occurs between partons inside initial-state jets rather than inside protons. The proper description of these initial-state jets requires ``beam functions''. In this talk I discuss a new factorization theorem with beam functions for the scenario of "isolated Drell-Yan" pp -> X l^+l^-, where X is restricted to contain no central jets. I also discuss the properties of the beam functions and how they can be related to the standard PDFs at a smaller perturbative scale.