  We consider sign changes of Fourier coefficients of Hecke-Maass cusp forms
for the group $\mathrm{SL}_3(\mathbb Z)$. When the underlying form is
self-dual, we show that there are $\gg_\varepsilon X^{5/6-\varepsilon}$ sign
changes among the coefficients $\{A(m,1)\}_{m\leq X}$ and that there is a
positive proportion of sign changes for many self-dual forms. Similar result
concerning the positive proportion of sign changes also hold for the
real-valued coefficients $A(m,m)$ for generic $\mathrm{GL}_3$ cusp forms, a
result which is based on a new effective Sato-Tate type theorem for a family of
$\mathrm{GL}_3$ cusp forms we establish. In addition, non-vanishing of the
Fourier coefficients is studied under the Ramanujan-Petersson conjecture.
