Ensembles of quantum chaotic systems are expected to exhibit random matrix universality in their energy spectrum. The presence of this universality can be diagnosed by looking for a linear in time 'ramp' in the spectral form factor, but for realistic systems this feature is typically only visible after a sufficiently long time. I will discuss several developments in our understanding of this intermediate time regime in the spectral form factor. First, I will describe a hybrid system in which the single particle levels are chaotic while the many-body levels are those of non-interacting particles. In this case, the linear ramp is replaced by an exponential ramp. Interacting deformations of the system can then lead to full many-body quantum chaos, but the approach to a linear ramp can be slow due to the presence of nearly conserved modes. Motivated by this problem, I will present a theory of the spectral form factor in systems with slow modes and will apply the results to a variety of hydrodynamic systems. Joint work with Mike Winer and Shaokai Jian.