Abstract: Events that occur on very long timescales are often the most interesting features of complicated dynamical systems. Even when we are able to reach the required timescales with a sufficiently accurate computer simulation, the resulting high dimensional data is difficult to mine for useful information about the event of interest. Over the past two decades, substantial progress has been made in the development of tools aimed at turning trajectory data into useful understanding of long-timescale processes. I will begin by describing one of the most popular of these tools, the variational approach to conformational dynamics (VAC). VAC involves approximating the eigenfunctions corresponding to large eigenvalues of the transition operator of the Markov process under study. These eigenfunctions encode the most slowly decorrelating functions of the system. I will describe our efforts to close significant gaps in the mathematical understanding of VAC error. A second part of the talk will focus on a family of methods very closely related to VAC that aim to compute predictions of specific long timescale phenomena (i.e. rare events) using only relatively short trajectory data (e.g. much shorter than the return time of the event). I will close by presenting a few questions for future numerical analysis.