Liouville type theorems for non-linear differential inequalities on Carnot groups

We overview some recent results on the existence and non-existence of positive solutions for differential inequalities of the kind
$$
\operatorname{div}_{0}\left(\frac {\varphi(|\nabla_{0}u|)}{|\nabla_{0}u|}\nabla_{0}u\right)\geqslant f(u)\ell(|\nabla_{0}u|)
$$
in the setting of Carnot groups under the Keller-Osserman condition.