We use first-principles calculations to study structural, vibrational, and superconducting properties of H_{2}S at pressures P≥200  GPa. The inclusion of zero-point energy leads to two different possible dissociations of H2S, namely 3H2S→2H3S+S and 5H2S→3H3S+HS2, where both H3S and HS2 are metallic. For H3S, we perform nonperturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction (λ≈2.64 at 200 GPa) and Tc. Anharmonicity hardens H─S bond-stretching modes and softens H─S bond-bending modes. As a result, the electron-phonon coupling is suppressed by 30% (λ≈1.84 at 200 GPa). Moreover, while at the harmonic level Tc decreases with increasing pressure, the inclusion of anharmonicity leads to a Tc that is almost independent of pressure. High-pressure hydrogen sulfide is a strongly anharmonic superconductor.