A substantial off-shell Higgs boson signal in the gluon fusion and vector boson fusion H --> ZZ and H --> WW channels at the Large Hadron Collider (LHC) facilitates a novel, complementary approach to constraining the total Higgs width Gamma_H. With LHC Run 1 data, experimental analyses by CMS and ATLAS find Gamma_H < 5.4 Gamma_H,SM and Gamma_H < [4.5,7.5] Gamma_H,SM at 95% confidence level, respectively, where Gamma_H,SM is the expected value in the Standard Model at the measured Higgs boson mass. I review the theoretical basis of the new approach and discuss its significance in comparison to other methods to bound and measure the Higgs width at the LHC and future colliders.