The perturbative quantum chromodynamics(PQCD) approach based on k_T factorization hasresulted in great achievements in the QCD calculation of hadronic B decays. Byregulating the endpoint divergence by the transverse momentum of quarks in thepropagators, one can perform the perturbation calculation for various diagrams,including annihilation type diagrams. In this paper, we review the currentstatus of the PQCD factorization calculation of two-body charmless B→PP, PV, VVUdecays up to next-to-leading order (NLO) QCD corrections. Two new powersuppressed terms in the decaying amplitudes are also considered. Usinguniversal input (non-perturbative) parameters, we collect the branching ratiosand CP asymmetry parameters of all charmless two body Bdecays, which are calculated in the PQCD approach up to NLO. The results are comparedwith those of the QCD factorization approach, soft-collinear effective theoryapproach, and current experimental measurements. For most of the considered Bmeson decays, the PQCD results for branching ratios agree well with those ofother approaches and experimental data. The PQCD predictions for the CP asymmetryparameters of many of the decay channels do not agree with those of otherapproaches but have better agreement with experimental data. Thelongstanding kπ puzzle regarding the pattern of the direct CPasymmetries of penguin-dominated B→kπ decays can beunderstood after the inclusion of NLO contributions in PQCD. The NLOcorrections and power suppressed terms play an important role in colorsuppressed and pure annihilation type B decay modes. These rare decays are moresensitive to different types of corrections, providing an opportunity toexamine the factorization approach with more precise experimental measurements.