  The objective of the present paper is to give a survey of recent progress on
applications of the approaches of Ringel-Hall type algebras to quantum groups
and cluster algebras via various forms of Green's formula. In this paper, three
forms of Green's formula are highlighted, (1) the original form of Green's
formula \cite{Green}\cite{RingelGreen}, (2) the degeneration form of Green's
formula \cite{DXX} and (3) the projective form of Green's formula
\cite{XX2007a} i.e. Green formula with a $\bbc^{*}$-action.
