How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem. The computational burden of probabilistic security assessment is even more unimaginable. In order to solve such problems, a security region (SR) methodology is proposed, which is a brand-new methodology developed on the basis of the classical point-wise method. Tianjin University has been studying the SR methodology since the 1980s, and has achieved a series of original breakthroughs that are described in this paper. The integrated SR introduced in this paper is mainly defined in the power injection space, and includes SRs to ensure steady-state security, transient stability, static voltage stability, and small-disturbance stability. These SRs are uniquely determined for a given network topology (as well as location and clearing process for transient faults) and given system component parameters, and are irrelevant to operation states. This paper presents 11 facts and related remarks to introduce the basic concepts, composition, dynamics nature, and topological and geometric characteristics of SRs. It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way. Thus, this article provides support for the systematic understanding, future research, and applications of SRs. The most critical finding on the topological and geometric characteristics of SRs is that, within the scope of engineering concern, the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes. Based on this finding, the calculation time for power system probabilistic security assessment (i.e., risk analysis) and power system optimization with security constraints can be decreased by orders of magnitude.