The VERITAS array of 12-m atmospheric-Cherenkov telescopes in southern Arizona began full-scale operations in 2007, and is one of the worlds most-sensitive detectors of astrophysical VHE (E>100 GeV) gamma rays. Approximately 50 blazars are known to emit VHE photons, and observations of blazars are a major focus of the VERITAS Collaboration. Nearly 2000 hours have been devoted to this program and ~130 blazars have already been observed with the array, in most cases with the deepest-ever VHE exposure. These observations have resulted in 21 detections, including 10 VHE discoveries. Recent highlights of the VERITAS blazar observation program, and the collaborations long-term blazar observation strategy, are presented.