The primary motivation for studying knot theory is the immediate applications to 3 and 4 dimensional topology. This has led to the development of homology theories and other invariants meant to extract information in this context. However, there are much simpler topological invariants that arise naturally and, despite their simplicity, are incredibly difficult to calculate. We will discuss several such invariants including Seifert genus, slice genus, and unknotting number, as well as the methods used in proving things about them.