We review recent progress in the laser and microwave spectroscopy of antiprotonic helium atoms (pHe + ≡ e − − p − He ++ ) carried out at CERN's Antiproton Decelerator facility (AD). Laser transitions were here induced between Rydberg states (n, ) and (n ± 1, − 1) of pHe + (n ∼ 40 and n − 1 being the principal and orbital angular momentum quantum numbers of the antiproton orbit). Successive refinements in the experimental techniques improved the fractional precision on the pHe + frequencies from 3 parts in 10 6 to ∼1 part in 10 8 . These included a radiofrequency quadrupole decelerator, which reduced the energy of the antiprotons from 5.3 MeV (the energy of the beam emerging from AD) to ∼100 keV. This enabled the production of pHe + in ultra-low density targets, where collisional effects with other helium atoms are negligible. A continuous wave pulse-amplified dye laser, stabilized against a femtosecond optical frequency comb, was then used to measure the pHe + frequencies with ppb-scale precision. This progress in the experimental field was matched by similar advances in computing methods for evaluating the expected transition frequencies in three-body QED calculations. The comparison of experimental (ν exp ) and theoretical (ν th ) frequencies for seven transitions in p4 He + and five in p3 He + yielded an antiproton-to-electron mass ratio of m p/m e = 1836.152 674(5). This agrees with the known proton-to-electron mass ratio at the level of ∼2× 10 −9 . The experiment also set a limit on any CPT-violating difference between the antiproton and proton charges and masses, (Q p − |Q p|)/Q p ∼ (m p − m p)/m p < 2 × 10 −9 to a 90% confidence level. If on the other hand we assume the validity of the CPT invariance, the m p/m e result can be taken to be equal to m p /m e . This can be used as an input to future adjustments of fundamental constants. The hyperfine structure of a state in p4 He + has also been measured by microwave spectroscopy to a precision of 3 × 10 −5 . This corresponds to the accuracy of the most precise three-body QED calculations. Further increases in the experimental precision may soon yield an improvement in the value of the antiproton magnetic moment.