We carry out a theoretical investigation of the backward interaction optical parametric oscillator (OPO), in which one of the generated waves is counterpropagating with respect to the pump. We derive simple, self-consistent analytical formulas for the continuous-wave and pulsed regimes. While consistent with previous works on the continuous-wave regime, our study enables us to extend the analysis to the pulsed regime. In particular, we derive simple expressions of the oscillation build-up time, pulsed threshold, and efficiency, for the first time, to our knowledge. We also investigate the peculiar spectral features of the backward OPO when pumped with a narrow-linewidth pulsed radiation, in particular, the absence of tolerance to phase mismatch and the natural ability to emit two waves with a Fourier-transform-limited spectrum. A comparison with the conventional forward OPO is also carried out to emphasize the unique properties of the backward OPO.