The strong coupling expansion has been providing us an intuitiveinsight into the non-perturbative nature of QCD. It was revealedthat color-confinement and spontaneous breaking of the chiralsymmetry are well understood within the strong coupling expansionat zero and finite temperature and/or baryon chemical potential.Analytic achievements at strong coupling preceding numericalstudies at weak coupling still have significance as the guidelineto understand the numerical results from lattice simulations.Such analytic attempts are reviewed with the inclusion of recentdevelopments for the system at finite temperature and/or baryonchemical potential.