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Our target is to learn visual correspondence from unlabeled videos. We develop LIIR, a locality-aware inter-and intra-video reconstruction framework that fills in three missing pieces, i.e., instance discrimination, location awareness, and spatial compactness, of self-supervised correspondence learning puzzle. First, instead of most existing efforts focusing on intra-video self-supervision only, we exploit cross video affinities as extra negative samples within a unified, inter-and intra-video reconstruction scheme. This enables instance discriminative representation learning by contrasting desired intra-video pixel association against negative inter-video correspondence. Second, we merge position information into correspondence matching, and design a position shifting strategy to remove the side-effect of position encoding during inter-video affinity computation, making our LIIR location-sensitive. Third, to make full use of the spatial continuity nature of video data, we impose a compactness-based constraint on correspondence matching, yielding more sparse and reliable solutions. The learned representation surpasses self-supervised state-of-the-arts on label propagation tasks including objects, semantic parts, and keypoints.