  In this paper, we study global properties of continuous plurisubharmonic
functions on complete noncompact K\"ahler manifolds with nonnegative
bisectional curvature and their applications to the structure of such
manifolds. We prove that continuous plurisubharmonic functions with reasonable
growth rate on such manifolds can be approximated by smooth plurisubharmonic
functions through the heat flow deformation. Optimal Liouville type theorem for
the plurisubharmonic functions as well as a splitting theorem in terms of
harmonic functions and holomorphic functions are established. The results are
then applied to prove several structure theorems on complete noncompact
K\"ahler manifolds with nonnegative bisectional or sectional curvature.
