Because computational storage space is finite, the finite-difference time-domain (FDTD) problem space size is finite and needs to be truncated by special boundary conditions. In the previous chapters we discussed some examples for which the problem space is terminated by perfect electric conductor (PEC) boundaries. However, many applications, such as scattering and radiation problems, require the boundaries simulated as open space. The types of special boundary conditions that simulate electromagnetic waves propagating continuously beyond the computational space are called absorbing boundary conditions (ABCs). However, the imperfect truncation of the problem space will create numerical reflections, which will corrupt the computational results in the problem space after certain amounts of simulation time. So far, several various types of ABCs have been developed. However, the perfectly matched layer (PML) introduced by Berenger [15, 16] has been proven to be one of the most robust ABCs [17-20] in comparison with other techniques adopted in the past. PML is a finite-thickness special medium surrounding the computational space based on fictitious constitutive parameters to create a wave-impedance matching condition, which is independent of the angles and frequencies of the wave incident on this boundary. The theory and implementation of the PML boundary condition are illustrated in this chapter.