  The goal of this paper has two-folds. First, we establish skeleton and spine
decompositions for superprocesses whose underlying processes are general
symmetric Hunt processes. Second, we use these decompositions to obtain weak
and strong law of large numbers for supercritical superprocesses where the
spatial motion is a symmetric Hunt process on a locally compact metric space
$E$ and the branching mechanism takes the form
$$\psi_{\beta}(x,\lambda)=-\beta(x)\lambda+\alpha(x)\lambda^{2}+\int_{(0,{\infty})}(e^{-\lambda
y}-1+\lambda y)\pi(x,dy)$$ with $\beta\in\mathcal{B}_{b}(E)$, $\alpha\in
\mathcal{B}^{+}_{b}(E)$ and $\pi$ being a kernel from $E$ to $(0,{\infty})$
satisfying $\sup_{x\in E}\int_{(0,{\infty})} (y\wedge y^{2})
\pi(x,dy)<{\infty}$. The limit theorems are established under the assumption
that an associated Schr\"{o}dinger operator has a spectral gap. Our results
cover many interesting examples of superprocesses, including super
Ornstein-Uhlenbeck process and super stable-like process. The strong law of
large numbers for supercritical superprocesses are obtained under the
assumption that the strong law of large numbers for an associated supercritical
branching Markov process holds along a discrete sequence of times, extending an
earlier result of Eckhoff, Kyprianou and Winkel [Ann. Probab.,43(5),
2594--2659, 2015] for superdiffusions to a large class of superprocesses. The
key for such a result is due to the skeleton decomposition of superprocess,
which represents a superprocess as an immigration process along a supercritical
branching Markov process.
