Secant varieties are classical objects in algebraic geometry, with many of their properties, such as their defining equations and singularities, being of interest for a very long time. Recently there has been interest in the Hodge theory of these varieties. I will review some classical Hodge theory and briefly explain how these ideas lift to a suitable derived category. We will apply some of the well-known theorems in this setting to make explicit Hodge theoretic computations for higher secant varieties of curves. In particular I will compute their intersection cohomology and describe the so-called trivial Hodge module. We will then zoom in on the special case of secant varieties of rational normal curves. Here we are able to exploit the defining equations to describe the nearby and vanishing cycle sheaves on the secant varieties. This talk is based on the work in my PhD thesis.