We review the recent progress in studying the anomalous electroweak quartic gauge boson couplings (QGBCs) at the LHC and the next generation high energy e+-e- linear colliders (LCs). The main focus is put onto the strong electroweak symmetry breaking scenario in which the non-decoupling guarantees sizable new physics effects for the QGBCs. After commenting upon the current low energy indirect bounds and summarizing the theoretical patterns of QGBCs predicted by the typical resonance/non-resonance models, we review our systematic model-independent analysis on bounding them via WW-fusion and WWZ/ZZZ-production. The interplay of the two production mechanisms and the important role of the beam-polarization at the LCs are emphasized. The same physics may be similarly and better studied at a multi-TeV muon collider with high luminosity.

Invited talk presented at the Workshop on " Physics at the First Muon Collider and at the Front End of a Muon Collider ", November 6-9, 1997, at Fermi National Accelerator Laboratory, Batavia, IL, USA. To be published in the conference proceedings, eds. S. Geer and R. Raja. (Latex, 17pp, 5eps-Figs, use aipproc.sty)