Recent advances in probing and controlling ultracold atomic gases have allowed access to rich physics from the realm of condensed matter. In the first part of this talk, I will describe quantum gas microscopy, a new tool for imaging and manipulating strongly interacting quantum gases containing thousands of atoms at the single atom level. I will describe its application to studying quantum phase transitions of Mott insulators and quantum magnets in bosonic systems of atoms. In the second part of the talk, I will shift focus to topological physics in fermionic systems. I will present experiments where we probe solitons created in fermionic superfluids across the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluidity. A surprising finding is that the mass of the solitons can be up to an order of magnitude larger than predicted. In the BEC regime, this can be explained by a concentration of quantum fluctuations in the soliton while in the BCS regime, it is due to Andreev bound states residing in the soliton. While these edge states are not topologically protected, Majorana bound states with topological protection can be realized with the addition of spin-orbit coupling we have recently demonstrated in spin-polarized Fermi gases. I will conclude with an outlook on how ultracold atoms can be used to study and manipulate edge states in topological superfluids.