  We present a theory for single- and two-phonon charge carrier scattering in
anisotropic two-dimensional semiconductors applied to single-layer black
phosphorus (BP). We show that in contrast to graphene, where two-phonon
processes due to the scattering by flexural phonons dominate at any practically
relevant temperatures and are independent of the carrier concentration $n$,
two-phonon scattering in BP is less important and can be considered negligible
at $n\gtrsim10^{13}$ cm$^{-2}$. At smaller $n$, however, phonons enter in the
essentially anharmonic regime. Compared to the hole mobility, which does not
exhibit strong anisotropy between the principal directions of BP
($\mu_{xx}/\mu_{yy}\sim1.4$ at $n=10^{13}$ cm$^{-2}$ and $T=300$ K), the
electron mobility is found to be significantly more anisotropic
($\mu_{xx}/\mu_{yy}\sim6.2$). Absolute values of $\mu_{xx}$ do not exceed 250
(700) cm$^2$V$^{-1}$s$^{-1}$ for holes (electrons), which can be considered as
an upper limit for the mobility in BP at room temperature.
