Finite subgroup of Cremona group is a classical topic in algebraic geometry since the 19th century.  In this talk we explain an extension of this problem to the symplectic category.  In particular, we will explain the symplectic counterparts of two classical theorems.  The first one due to Noether, says a plane Cremona map is decomposed into a sequence of quadratic transformations, which is generalized to the symplectic category on the homological level.  The second one is due to Castelnuovo and Kantor, which says a minimal G-surface either has a conic bundle structure or is a Del Pezzo surface.  The latter theorem lies the ground of classifications of finite Cremona subgroups due to Dolgachev and Iskovskikh.  This is an ongoing program joint with Weimin Chen and Tian-Jun Li