We perform frequentist and Bayesian statistical analyses of Higgs- and Z-portal models of dark matter particles with spin 0, 1⁄2 and 1. Our analyses incorporate data from direct detection and indirect detection experiments, as well as LHC searches for monojet and monophoton events, and we also analyze the potential impacts of future direct detection experiments. We find acceptable regions of the parameter spaces for Higgs-portal models with real scalar, neutral vector, Majorana or Dirac fermion dark matter particles, and Z-portal models with Majorana or Dirac fermion dark matter particles. In many of these cases, there are interesting prospects for discovering dark matter particles in Higgs or Z decays, as well as dark matter particles weighing 100 GeV. Negative results from planned direct detection experiments would still allow acceptable regions for Higgs- and Z-portal models with Majorana or Dirac fermion dark matter particles.