Abstract: Smale's 13th problem is about finding a uniform upper bound on the number of limit cycles of classical Lienard systems $(x',y')=(y-F(x),-x)$. We present an overview of the method of dealing with this problem using geometric singular perturbation theory, show the progress that was already made, and also indicate the huge difficulties that lie ahead.  We then proceed to talk about work in progress aimed at providing a slow-fast version of a 2008 result by Dumortier and Caubergh, i.e. we target uniform finite cyclicity of unbounded slow-fast cycles. At the moment it is joint work with my PhD student Melvin Yeung.