  We study viscosity solutions to complex hessian equations. In the local case,
we consider $\Omega$ a bounded domain in $\mathbb{C}^n,$ $\beta$ the standard
K\"{a}hler form in $\mathcal{C}^n$ and $1\leq m\leq n.$ Under some suitable
conditions on $F, g$, we prove that the equation $(dd^c
\varphi)^m\wedge\beta^{n-m}=F(x,\varphi)\beta^n,\ \f=g$ on $\pO$ admits a
unique viscosity solution modulo the existence of subsolution and
supersolution. If moreover, the datum are H\"{o}lder continuous then so is the
solution. In the global case, let $(X,\omega)$ be a compact hermitian
homogeneous manifold where $\omega$ is an invariant hermitian metric (not
necessarily K\"{a}hler). We prove that the equation
$(\omega+dd^c\varphi)^m\wedge\omega^{n-m}=F(x,\varphi)\omega^n$ has a unique
viscosity solution under some natural conditions on $F.$
