We will describe Choquet and strong Choquet spaces and provide proofs of some of their basic properties as well as their relation to Baire spaces and completeness. This will give us a characterization of when metric spaces are complete, provide an alternative proof of Hausdorff and Sierpinski's theorems on continuous open images of complete metric spaces, and result in a characterization of Polish spaces similar to the Urysohn Metrization Theorem that is of interest in descriptive set theory. This talk will assume only a standard course in topology and no background in logic should be needed.