This work presents the aerodynamic topology optimization of high-pressure turbine rotor blade tips. Before carrying out the topology optimization on the blade tip, some initial tip design studies were carried out. A winglet tip was optimized first and it was found that the optimum winglet design features a combination of small and largest overhangs possible that increase the aerodynamic efficiency by 1.40% compared to the datum design. Second, a radial basis function-based parametrization was set up to allow the creation of a single squealer rim on the datum blade’s tip that could move position in the circumferential direction. The optimum case proved to increase efficiency by 0.46% compared to the flat datum tip of the same tip gap. After that, a combination of winglet and topology free squealer tips was investigated via topology optimization. The winglet tip was created as in the winglet-only optimization cases and topology free squealer walls were parametrized and created using mapping of a radial basis function surface. It was shown that the radial basis function surface-based parametrization creates a very flexible design space containing novel squealer topologies. Combining both winglet and novel squealer topology optimization, better designs than the flat tip winglet can be achieved. However, because of the flexibility of the design space, gradient-based methods were found to struggle to reach an optimum solution. This was resolved by optimizing the most promising design subspace.