We present FiFTy, a modern file type identification tool for memory forensics and data carving. In contrast to previous approaches based on hand-crafted features, we design a compact neural network architecture, which uses a trainable embedding space, akin to successful natural language processing models. Our approach dispenses with explicit feature extraction which is a bottleneck in legacy systems. We evaluate the proposed method on a novel dataset with 75 file types - the most diverse and balanced dataset reported to date. FiFTy consistently outperforms all baselines in terms of speed, accuracy and individual misclassification rates. We achieved an average accuracy of 77.5% with processing speed of approx 38 sec/GB, which is better and more than an order of magnitude faster than the previous state-of-the-art tool - Sceadan (69% at 9 min/GB). Our tool and the corresponding dataset are available publicly online.