This is an open-label (physicians and participants know the identity of the assigned treatment), randomized (the study medication is assigned by chance), multicenter, active-controlled study comparing daratumumab, VELCADE, and dexamethasone (DVd) with VELCADE and dexamethasone (Vd) in participants with relapsed or refractory multiple myeloma. Approximately 480 participants will be randomly assigned in a 1:1 ratio to receive either DVd or Vd. Randomization will be stratified by International Staging System (ISS), number of prior treatment programs (1 vs. 2 or 3 vs. >3), and prior VELCADE treatment ("no" vs. "yes"). Within each stratum, participants will be randomized to one of the treatment groups.The study will consist of a Screening Phase, a Treatment Phase, and a Follow-up Phase. Participants will be treated until disease progression, unacceptable toxicity, or other reasons to discontinue the study.