Abstract Single molecule localization microscopy (SMLM) has revolutionized biological imaging, improving the spatial resolution of traditional microscopes by an order of magnitude. However, SMLM techniques depend on accumulation of many localizations over thousands of recorded frames to yield a single super-resolved image, which is time consuming. Hence, the capability of SMLM to observe dynamics has always been limited. Typically, a few minutes of data acquisition are needed to reconstruct a single super-resolved frame. In this work, we present DBlink, a novel deep-learning-based algorithm for super spatiotemporal resolution reconstruction from SMLM data. The input to DBlink is a recorded video of single molecule localization microscopy data and the output is a super spatiotemporal resolution video reconstruction. We use bi-directional long short term memory (LSTM) network architecture, designed for capturing long term dependencies between different input frames. We demonstrate DBlink performance on simulated data of random filaments and mitochondria-like structures, on experimental SMLM data in controlled motion conditions, and finally on live cell dynamic SMLM. Our neural network based spatiotemporal interpolation method constitutes a significant advance in super-resolution imaging of dynamic processes in live cells.