General human action recognition requires understanding of various visual cues. In this paper, we propose a network architecture that computes and integrates the most important visual cues for action recognition: pose, motion, and the raw images. For the integration, we introduce a Markov chain model which adds cues successively. The resulting approach is efficient and applicable to action classification as well as to spatial and temporal action localization. The two contributions clearly improve the performance over respective baselines. The overall approach achieves state-of-the-art action classification performance on HMDB51, J-HMDB and NTU RGB+D datasets. Moreover, it yields state-of-the-art spatio-temporal action localization results on UCF101 and J-HMDB.