We study hot-electron cooling by acoustic and optical phonons in monolayer MoS2. The cooling power P (Pe=P/n) is investigated as a function of electron temperature Te (0-500 K) and carrier density n (1010-1013 cm-2) taking into account all relevant electron-phonon (el-ph) couplings. We find that the crossover from acoustic phonon dominated cooling at low Te to optical phonon dominated cooling at higher Te takes place at Te∼50–75 K. The unscreened deformation potential (DP) coupling to the TA phonon is shown to dominate P due to acoustic phonon scattering over the entire temperature and density range considered. The cooling power due to screened DP coupling to the LA phonon and screened piezoelectric (PE) coupling to the TA and LA phonons is orders of magnitude lower. In the Bloch-Grüneisen (BG) regime, P∼Te4 (Te6) is predicted for unscreened (screened) el-ph interaction and P∼n-1/2 (Pe∼n-3/2) for both unscreened and screened el-ph interaction. The cooling power due to optical phonons is dominated by zero-order DP couplings and the Fröhlich interaction, and is found to be significantly reduced by the hot-phonon effect when the phonon relaxation time due to phonon-phonon scattering is large compared to the relaxation time due to el-ph scattering. The Te and n dependence of the hot-phonon distribution function is also studied. Our results for monolayer MoS2 are compared with those in conventional two-dimensional electron gases (2DEGs) as well as monolayer and bilayer graphene.