The task of retrieving video content relevant to natural language queries plays a critical role in effectively handling internet-scale datasets. Most of the existing methods for this caption-to-video retrieval problem do not fully exploit cross-modal cues present in video. Furthermore, they aggregate per-frame visual features with limited or no temporal information. In this paper, we present a multi-modal transformer to jointly encode the different modalities in video, which allows each of them to attend to the others. The transformer architecture is also leveraged to encode and model the temporal information. On the natural language side, we investigate the best practices to jointly optimize the language embedding together with the multi-modal transformer. This novel framework allows us to establish state-of-the-art results for video retrieval on three datasets. More details are available at http://thoth.inrialpes.fr/research/MMT.