We demonstrate a novel deep neural network capable of reconstructing human full body pose in real-time from 6 Inertial Measurement Units (IMUs) worn on the users body. In doing so, we address several difficult challenges. First, the problem is severely under-constrained as multiple pose parameters produce the same IMU orientations. Second, capturing IMU data in conjunction with ground-truth poses is expensive and difficult to do in many target application scenarios (e.g., outdoors). Third, modeling temporal dependencies through non-linear optimization has proven effective in prior work but makes real-time prediction infeasible. To address this important limitation, we learn the temporal pose priors using deep learning. To learn from sufficient data, we synthesize IMU data from motion capture datasets. A bi-directional RNN architecture leverages past and future information that is available at training time. At test time, we deploy the network in a sliding window fashion, retaining real time capabilities. To evaluate our method, we recorded DIP-IMU, a dataset consisting of $10$ subjects wearing 17 IMUs for validation in $64$ sequences with $330,000$ time instants; this constitutes the largest IMU dataset publicly available. We quantitatively evaluate our approach on multiple datasets and show results from a real-time implementation. DIP-IMU and the code are available for research purposes.