In this talk, I will begin with introducing the method of
pseudo-holomorphic curves (which are defined by Cauchy-Riemnn type elliptic
systems) in the study of symplectic and contact topology. Then I will focus
on discussing the one studied by Yong-Geun Oh and myself recently, including
its potential, drawbacks and possible improvements towards the goal of a
better understanding in contact topology. (The similar elliptic system named
the generalized pseudo-holomorphic curves in symplectizations was introduced
by Hofer and studied by Abbas-Cieliebak-Hofer, Abbas in the proposal of
proving the Weinstein conjecture for dimension three.)