Encoding information in the time-frequency domain demonstrates its potential for quantum information processing. It offers a novel scheme for communications with large alphabets, computing with large quantum systems, and new approaches to metrology. It is then crucial to secure full control on the generation of time-frequency quantum states and their properties. Here, the authors present an overview of the theoretical background and the technical aspects related to the characterization of time-frequency properties of two-photon states. The authors provide a detailed account of the methodologies that have been implemented for measuring frequency correlations and for the retrieval of the full spectral wavefunction. This effort has benefited enormously from the adaptation of classical metrology schemes to the needs of operating at the single-photon level.