Chiral and U_A(1) symmetry in correlation functions in medium

In this review, we will discuss how the chiral symmetry and U_A(1) breaking effects are reflected in the correlation functions. Using the Banks-Casher formula, one can identify the density of zero eigenvalues to be the common ingredient that governs the chiral symmetry breaking in correlation functions between currents composed of light quarks with or without a heavy quark. Similarly the presence of the U_A(1) breaking effect is determined through the contribution of the topologically non trivial configurations that depends on the number of flavors. We also discuss how the symmetry breaking effects are reflected in the gluon correlation functions. Finally, we review the Witten Veneziano formula for the eta' mass in medium.