Superconducting materials hold the promise of revolutionizing modern technology. Their implementation is, however, held back by the low temperatures required for superconductivity to exist. At the same time, a special kind of superconductivity – topological superconductivity – may greatly improve the accuracy of quantum computers, possibly revolutionizing search and security algorithms. Realizing the ultimate goals of room-temperature superconductivity and topological quantum computing requires advancements in the field of (nano)materials science. In particular, materials – or combinations of different materials – should be discovered or engineered. One strategy therein is to combine two materials in verticals stacks, so-called heterostructures. This thesis describes the investigation of different superconducting heterostructures by scanning tunneling microscopy (STM) – an analysis technique unmatched in its capabilities to characterize materials with atomic resolution. The research presented in this thesis explores three avenues to increase our understanding of superconducting materials. Firstly, we report on our method to measure shot noise in the STM with high accuracy. It is shown that the effective charge can be determined with a precision better than 5% of an electron charge for current down to 0.1 nA. Secondly, we report on the growth and characterization of the high-temperature superconductor 1-UC FeSe / SrTiO₃. In this work, key preparation challenges are identified, and a superconducting sample was prepared. Lastly, STM measurement of heterostructures consisting of the magnetic insulators CrX₃ (X = Cl, Br) and the superconductor NbSe₂ are described. In both material systems, we observed Yu-Shiba-Rusinov edge states to exist. For CrBr₃/NbSe₂, this challenges the previously reported signs of topological superconductivity. The dI/dV measurements are supported by DFT simulations and shot noise measurements. Overall, the findings presented in this thesis represent small but essential fragments of the larger, still-emerging picture of superconductivity. Additionally, specific research directions are identified, such as the application of high-accuracy shot noise measurements to ill-understood superconducting materials and heterostructures.