We report inclusive and exclusive measurements for χc1 and χc2 production in B decays. We measure B(B→χc1X)=(3.03±0.05(stat)±0.24(syst))×10-3 and B(B→χc2X)=(0.70±0.06(stat)±0.10(syst))×10-3. For the first time, χc2 production in exclusive B decays in the modes B0→χc2π-K+ and B+→χc2π+π-K+ has been observed, along with first evidence for the B+→χc2π+KS0 decay mode. For χc1 production, we report the first observation in the B+→χc1π+π-K+, B0→χc1π+π-KS0 and B0→χc1π0π-K+ decay modes. Using these decay modes, we observe a difference in the production mechanism of χc2 in comparison to χc1 in B decays. In addition, we report searches for X(3872) and χc1(2P) in the B+→(χc1π+π-)K+ decay mode. The reported results use 772×106 BB-events collected at the (4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.