  Pseudo-holomorphic curves on almost complex manifolds have been much more
intensely studied than their "dual" objects, the plurisubharmonic functions.
These functions are defined classically by requiring that the restriction to
each pseudo-holomorphic curve is subharmonic. In this paper subharmonic
functions are defined by applying the viscosity approach to a version of the
complex hessian which exists intrinsically on any almost complex manifold.
  Three theorems are proved. The first is a restriction theorem which
establishes the equivalence of our definition with the "classical" definition.
In the second theorem, using our "viscosity" definitions, the Dirichlet problem
is solved for the complex Monge-Amp\`ere equation in both the homogeneous and
inhomogeneous forms. These two results are based on theorems found in two
recent papers of the authors. Finally, it is shown that the plurisubharmonic
functions considered here agree with the plurisubharmonic distributions. In
particular, this proves a conjecture of Nefton Pali.
