This chapter presents an extended FDTD algorithm for the analysis of arbitrarily-shaped dielectric and dispersive media. The conventional FDTD algorithm is formulated using Yee’s mesh, which has difficulty of modeling arbitrarily-shaped media such as rods and spheres. When analyzing these structures, we need to use small spatial sampling grids, which results in long computation time, particularly for three-dimensional (3-D) problems. To alleviate this problem, we extend the contour-path effective-permittivity (CP-EP) algorithm to a 3-D problem. The CP-EP algorithm has the advantage that Yee’s mesh is used as it is, and a computational cell partially filled with dielectric media can be considered with a relatively large grid. The formulation is given for fourteen cases of the partially filled cells with curved interfaces. A dielectric sphere is analyzed to demonstrate the effectiveness of the CP-EP algorithm relative to the conventional staircase approximation. We also consider 3-D dispersive media. The dispersive contour pass (DCP) algorithm, which was first applied to the Z transform technique in two-dimensional (2-D) problems, is extended to the FDTD method along with the trapezoidal recursive convolution (TRC) technique. We formulate the 3-D DCP-FDTD method based on the TRC technique for the analysis of the Drude-Lorentz model. Through the analysis of a metallic sphere, the results are found to be close to the Mie solution, rather than the staircase approximation. In addition, the staircase approximation shows spurious filed along the metal surface, while the DCP algorithm provides field distributions with suppressed spurious field.