The dynamics of droplets impacting surfaces at high speed are not only fascinating from a fundamental perspective, but they are also important for a variety of applications including spray processes, forensics, and inkjet printing. We are especially interested in cases where droplets break up, with a view to reducing the formation of small fast secondary droplets with indiscriminate trajectories (splashing). In this talk, we will consider two such surfaces from our recent and current projects: dry curved substrates (spheres and concave surfaces) and shallow pools. For the former, using high-speed imaging experiments we have shown that it is harder for droplets to splash on small spheres during axisymmetric impact. We propose a physical mechanism to explain this behaviour and incorporate it into state-of-the-art splashing theory to attain a consistent parameterisation of the splashing threshold across dry concave, convex, and flat surfaces. We will briefly touch-on some effects of asymmetry using unpublished color high-speed imaging results. On shallow pools, we have uncovered a well-defined depth transition that strongly affects both the propensity for, and dynamics of, splashing at high Reynolds number. This transition will be delineated throughout a wide Weber number/pool depth parameter space, using numerical simulations to reveal the underlying physics. We will examine the incredibly diverse range of dynamics that can occur and compare the results to those seen on the dry (curved) surfaces discussed prior.