Singular moduli is the classical name for the values of the $j$ function at imaginary quadratic irrationalities. They are algebraic numbers that play an important role in number theory and have been studied since Kronecker and Weber. In the 1990s Borcherds and Zagier established some beautiful connections between the traces of singular moduli, infinite products and weakly holomorphic modular forms of half-integral weight. In this talk I will report on joint work with W. Duke and A. Toth where we consider cycles integrals of the $j$ function, which can be thought as real quadratic analogues of singular moduli.