The recent discovery of topological insulators as a new class of quantum matter offers appealing schemes for potential definitive realization of topological superconductors and unambiguous detection of Majorana fermions. In this talk, I will attempt to give an overview on the recent advances and latest excitements in this vibrant area, with some of our own stories surrounding low-dimensional topological superconductors and even high transition temperature superconductors squeezed in. Our first focus is on systems that rely on proximity effects; here we will show that proper introduction of dilute magnetic dopants at the interfaces of topological insulators and conventional superconductors can effectively convert the systems into chiral topological superconductors. Next we shift to intrinsic systems, exploring how Rashba spin-orbit coupling and van Hove singularity could induce exotic topological phase transitions within the context of “correlation of correlations”. Beyond such microscopic model studies, we will also use first-principles approaches to identify candidate systems that promise to materialize 2D topological superconductivity. In doing so, we will highlight the importance of interfacial growth science in guiding predictive discoveries of new high-transition-temperature superconductors and topological superconductors.