The first measurements of the millimeter- and submillimeter (mm/submm)-wave rotational–torsional transitions in the v3= 1 ground torsional state (n= 0) of hydrogen peroxide are reported. The 149 newly measured transitions extend from 72 to 623 GHz in frequency and up to J= 32 and Ka= 3 in rotational quantum number. Additional measurements in the ground vibrational and torsional state around 1 THz are also reported. These data, along with all previously published microwave, mm/submm-wave, and far infrared data in the ground and v3= 1 vibrational state, along with recent infrared measurements, have been fitted simultaneously to their respective experimental uncertainties using a multi-state Hamiltonian that includes Fermi- and Coriolis-type interactions.