In the early 1990s, Zelditch adapted the Selberg trace formula to prove an effective version of Bowen's equidistribution theorem for closed geodesics on hyperbolic surfaces. Building on his approach, in joint work with Junehyuk Jung and Peter Zenz, we refined Zelditch's idea to achieve the optimal error term in the equidistribution of closed geodesics on compact hyperbolic surfaces. In this talk, we begin by reviewing the basic ideas of trace formulas, followed by a discussion of the new contributions. No prior knowledge of trace formulas is required.