This paper reviews recent work on receiver-side compensation of nonlinear impairments in optical fiber transmission. Intuitively, both linear and nonlinear impairments can be compensated since they are deterministic processes. In particular, fiber transmission can be modeled using the nonlinear Schrodinger equation that can be solved by the well-known split-step Fourier transform method and fiber impairment can be compensated by propagating the received signal backward in the digital domain. The first publication on digital backward propagation (DBP) also showed that the computation complexity can be met by the advances in DSP technology even if the split-step finite-impulse filtering method, which may be more suitable for real-time implementation.