Gauss's quadratic reciprocity law has been extensively generalized in multiple directions within number theory. This talk will begin with explicit examples of reciprocity laws, including an interpretation of the proof of Fermat’s Last Theorem by Wiles and Taylor-Wiles as a consequence of a reciprocity law. As part of this discussion, I will introduce modular forms, elliptic curves, and Galois representations, leading to an overview of the Langlands reciprocity. I will then discuss the role of congruences in the study of reciprocity laws, with a particular focus on the Serre weight conjectures. I will conclude by outlining the proof of the Serre weight conjectures for GSp4. This is partly based on joint work with Daniel Le and Bao Le Hung.