Abstract: Researchers in the field of numerical simulation of seismic wave motion have been suffering from the challenge in understanding and studying artificial boundary conditions (ABC), which is mainly attributed to the lack of systematic discussion and effective integration of ABC originating from various wave problems. To establish a systematic overall understanding of the essence of ABC and the basic performance of various specific ABC, we conducted a simple, intuitive, and logically clear discussion on the important issues of ABC, including their essence and primary methods, the theory of accuracy control, and numerical stability. ABC is essentially a collective name for all computation methods used to calculate the motion on an artificial boundary caused by out-going waves. The computational mode of ABC can be intuitively classified into three fundamental branches: space-time extrapolation, stress equilibrium on an artificial boundary, and regional attenuation. We discuss the similarities on the implementation pattern, the theory of accuracy control, and the numerical stability for the ABC in the same branch, as well as those discrepancies among different ABC branches. Consequently, a number of important issues associated with ABC are clarified, such as the following viewpoints. Liao’s time-space extrapolation rule is the most fundamental principle for the accuracy evaluations of all the extrapolation-type and stress-type ABC. The stability problem for Liao’s ABC applied in a finite-element wave motion simulation is mainly caused by the difficulty embedded in a combination of the boundary’s finite-difference-type formula and the inner-domain finite-element formula. Attenuation-type ABC provide an observation view angle that is completely different from that of extrapolation- and stress-type ABC; thus, they play an irreplaceable and unique role in artificial boundary problems.