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these data may be inaccurate for several reasons (e.g., inaccurate information of components datasheets and/or outdated topological information).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