Key operational and protection functions of power systems (e.g., optimal power flow scheduling and control, state estimation, protection, and fault location) rely on the availability of models to represent the system's behavior under different operating conditions. Power systems models require knowledge of the components' electrical parameters and the system topology. However, these data may be inaccurate for several reasons (e.g., inaccurate information of components datasheets and/or outdated topological information). The deployment of time synchronization in phasor measurement units (PMUs) and remote terminal units (RTUs) enables the collection of large datasets of synchronised measurements to infer power systems models and learn associated power flow constraints. Within this context, this paper presents a comprehensive review of measurement-based estimation methods for power flow models using time-synchronised measurements. It begins by exploring advancements in time dissemination technologies and the characterization of uncertainties in PMUs and instrument transformers, along with their implications for parameters estimation. The paper then examines the power system parameter estimation problem, highlighting key techniques and methodologies. In the following, the paper focuses on measurement models for state-independent power flow model estimation, including line parameters, admittance matrices, topology, and joint state-parameter estimation. Finally, the review discusses recent approaches for estimating state-dependent power flow models, with particular reference to linearized power flow approximations in view of their large use in control applications.