This is a survey of contact homology and its applications to the study of contact manifolds. It is a small tribute to Yasha Eliashberg's huge generosity with his countless explanations of his deep mathematical insights all along his career. It is also the author's wishful thinking that this text could be useful to students and young mathematicians for learning about some of the holomorphic curves based invariants in contact geometry.
Frédéric Bourgeois (Wed,) studied this question.