  In this paper, we prove strong subconvexity bounds for self-dual
$\mathrm{GL}(3)$ $L$-functions in the $t$-aspect and for
$\mathrm{GL}(3)\times\mathrm{GL}(2)$ $L$-functions in the
$\mathrm{GL}(2)$-spectral aspect. The bounds are strong in the sense that they
are the natural limit of the moment method pioneered by Xiaoqing Li, modulo
current knowledge on estimate for the second moment of $\rm GL(3)$
$L$-functions on the critical line.
