Local feature matching is a computationally intensive task at the subpixel level. While detector-based methods coupled with feature descriptors struggle in low-texture scenes, CNN-based methods with a sequential extract-to-match pipeline, fail to make use of the matching capacity of the encoder and tend to overburden the decoder for matching. In contrast, we propose a novel hierarchical extract-and-match transformer, termed as MatchFormer. Inside each stage of the hierarchical encoder, we interleave self-attention for feature extraction and cross-attention for feature matching, yielding a human-intuitive extract-and-match scheme. Such a match-aware encoder releases the overloaded decoder and makes the model highly efficient. Further, combining self- and cross-attention on multi-scale features in a hierarchical architecture improves matching robustness, particularly in low-texture indoor scenes or with less outdoor training data. Thanks to such a strategy, MatchFormer is a multi-win solution in efficiency, robustness, and precision. Compared to the previous best method in indoor pose estimation, our lite MatchFormer has only 45% GFLOPs, yet achieves a +1.3% precision gain and a 41% running speed boost. The large MatchFormer reaches state-of-the-art on four different benchmarks, including indoor pose estimation (ScanNet), outdoor pose estimation (MegaDepth), homography estimation and image matching (HPatch), and visual localization (InLoc).