The paper introduces Meep, a flexible and free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetic phenomena. Meep is designed to be full-featured, supporting various materials, boundary conditions, and advanced features such as advanced signal processing, subpixel averaging, and flexible scripting. The authors highlight the importance of Meep in addressing the limitations of commercial FDTD software and the need for open-source tools in research. The paper discusses the discretization and coordinate systems used in Meep, including the Yee grid and continuous coordinates, and explains how these are managed through grid chunks and boundary conditions. It also covers the implementation of subpixel averaging to improve accuracy and the handling of nonlinear and dispersive materials. Additionally, the paper details techniques for efficient computation of scattering spectra and resonant modes, emphasizing the versatility and performance of Meep in solving complex electromagnetic problems.The paper introduces Meep, a flexible and free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetic phenomena. Meep is designed to be full-featured, supporting various materials, boundary conditions, and advanced features such as advanced signal processing, subpixel averaging, and flexible scripting. The authors highlight the importance of Meep in addressing the limitations of commercial FDTD software and the need for open-source tools in research. The paper discusses the discretization and coordinate systems used in Meep, including the Yee grid and continuous coordinates, and explains how these are managed through grid chunks and boundary conditions. It also covers the implementation of subpixel averaging to improve accuracy and the handling of nonlinear and dispersive materials. Additionally, the paper details techniques for efficient computation of scattering spectra and resonant modes, emphasizing the versatility and performance of Meep in solving complex electromagnetic problems.