  We examine $L^p$-viscosity solutions to fully nonlinear elliptic equations
with bounded-measurable ingredients. By considering $p_0<p<d$, we focus on
gradient-regularity estimates stemming from nonlinear potentials. We find
conditions for local Lipschitz-continuity of the solutions and continuity of
the gradient. We briefly survey recent breakthroughs in regularity theory
arising from (nonlinear) potential estimates. Our findings follow from -- and
are inspired by -- fundamental facts in the theory of $L^p$-viscosity
solutions, and results in the work of Panagiota Daskalopoulos, Tuomo Kuusi and
Giuseppe Mingione [10].
