  Canonical duality-triality is a breakthrough methodological theory, which can
be used not only for modeling complex systems within a unified framework, but
also for solving a wide class of challenging problems from real-world
applications. This paper presents a brief review on this theory, its
philosophical origin, physics foundation, and mathematical statements in both
finite and infinite dimensional spaces, with emphasizing on its role for
bridging the gap between nonconvex analysis/mechanics and global optimization.
Special attentions are paid on unified understanding the fundamental
difficulties in large deformation mechanics, bifurcation/chaos in nonlinear
science, and the NP-hard problems in global optimization, as well as the
theorems, methods, and algorithms for solving these challenging problems.
Misunderstandings and confusions on some basic concepts, such as objectivity,
nonlinearity, Lagrangian, and generalized convexities are discussed and
classified. Breakthrough from recent challenges and conceptual mistakes by M.
Voisei, C. Zalinescu and his co-worker are addressed. Some open problems and
future works in global optimization and nonconvex mechanics are proposed.
