Heun equation is the second order differential equation with 4 regular singularities and it plays important role in theoretical physics. Unlike the hypergeometric equation, which has 3 regular singularities, the connection formulas for Heun equation don't have expressions in terms of elementary functions. Recently they were written in terms of semiclassical conformal blocks by Bonelli-Iossa-Lichtig-Tanzini. We derive these formulas using the interplay between Heun equations and Painlevé equations. This computation in particular provides the expression for the semiclassical conformal blocks within the Painlevé theory. This is the joint work with Harini Desiraju, Promit Ghosal, and Oleg Lisovyy.