Contact geometry is the study of geometric structures on odd dimensional smooth manifolds given by a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete non-integrability. The associated one form is called a contact form and uniquely determines a vector field called the Reeb vector field on the manifold. I will explain how one to make use of J-holomorphic curves to obtain a Floer theoretic contact invariant whose chain complex is generated by Reeb orbits. In particular, I will explain the pitfalls in defining contact homology and discuss joint work with Hutchings which gives a rigorous construction of cylindrical contact homology via geometric methods. This talk will feature lots of graphics to acclimate people to the realm of contact geometry.