K-stability is a stability for varieties (Tian, Donaldson), a modification of classical stability (Mumford). While it has been known for several decades that classically stability does not work in higher dimensions moduli construction, the author explains how the K-stability fits into recent construction of compact moduli of general type varieties by KSBA (Koll\'ar-Shepherd-Barron, Alexeev) theory. As the KSBA theory depends on MMP-based birational geometry, not on GIT, it also reflects more general compatibility between the K-stability and such birational algebraic geometry which really exists. If time permits, I explain some partial progress towards my dream "K-moduli", more general moduli via K-stability and cscK metrics.