The finite-difference time-domain (FDTD) method has been widely used for solving various electromagnetic problems involving electromagnetic radiation, propagation and scattering. This thesis presents the analysis and applications of FDTD methods for lossy and dispersive media. The stability analysis is first performed on Yee's explicit FDTD schemes for doubly lossy media whereby a generalized stability criterion applicable for all 3-D explicit FDTD schemes is found. Similarly, the 3-D dispersion analysis reveals some important dispersion characteristics of 3-D explicit FDTD schemes for doubly lossy media. The thesis next proposes a corrected impulse invariance method as the current classical impulse invariance method used in explicit FDTD for dispersive media is found to be inaccurate. A corrected Z-transform table is provided to facilitate the conversion from frequency to Z domain. With the aid of the table, various formulations of FDTD update equations can be carried out conveniently. For unconditionally stable alternating-direction-implicit FDTD (ADI-FDTD) method, Lyapunov and matrix norm stability analysis is applied on various ADI schemes for doubly lossy media. A rigorous analytical proof of unconditional stability is provided. Subsequently, a unified efficient fundamental ADI-FDTD (FADI-FDTD) schemes for lossy media is formulated. They are formulated in the simplest, most concise, most efficient, and most fundamental form of ADI-FDTD. Such efficient fundamental schemes have substantially less right-hand-side (RHS) update coefficients and field variables compared to the conventional ADI-FDTD schemes. Thus, they feature higher efficiency with reduced memory indexing and arithmetic operations. Further, the generalized formulation of FADI-FDTD method for dispersive media is provided. It is efficient, robust and applicable to Debye, Lorentz, Drude and complex conjugate pole-residue pair models.