The target of space-time video super-resolution (STVSR) is to increase the spatial-temporal resolution of low-resolution (LR) and low-frame-rate (LFR) videos. Recent approaches based on deep learning have made significant improvements, but most of them only use two adjacent frames, that is, short-term features, to synthesize the missing frame embedding, which cannot fully explore the information flow of consecutive input LR frames. In addition, existing STVSR models hardly exploit the temporal contexts explicitly to assist high-resolution (HR) frame reconstruction. To address these issues, in this article, we propose a deformable attention network called STDAN for STVSR. First, we devise a long short-term feature interpolation (LSTFI) module that is capable of excavating abundant content from more neighboring input frames for the interpolation process through a bidirectional recurrent neural network (RNN) structure. Second, we put forward a spatial-temporal deformable feature aggregation (STDFA) module, in which spatial and temporal contexts in dynamic video frames are adaptively captured and aggregated to enhance SR reconstruction. Experimental results on several datasets demonstrate that our approach outperforms state-of-the-art STVSR methods. The code is available at https://github.com/littlewhitesea/STDAN.