The strong coupling expansion has been providing us an intuitive insight into the non-perturbative nature of QCD. It was revealed that color-confinement and spontaneous breaking of the chiral symmetry are well understood within the strong coupling expansion at zero and finite temperature and/or baryon chemical potential. Analytic achievements at strong coupling preceding numerical studies at weak coupling still have significance as the guideline to understand the numerical results from lattice simulations. Such analytic attempts are reviewed with the inclusion of recent developments for the system at finite temperature and/or baryon chemical potential.