Georgia Institute of Technology College of Sciences

After, briefly, recalling the definition of contact homology, a powerful but somewhat intractable and still largely unexplored invariant of Legendrian knots in contact structures, I will discuss various ways of constructing more tractable and computable invariants from it. In particular I will discuss linearizations, products, massy products, A_\infty structures and terms in a spectral sequence. I will also show examples that demonstrate some of these invariants are quite powerful. I will also discuss what is known and not known about the relations between all of these invariants.