Abstract: (i) A powerful tool in regularity theory for PDEs is given by representation formulas: your solution is expressed by the convolution of the data of the equation with a kernel with known (good) properties. Regularity properties are therefore deduced by such an "explicit" formula. However, if the coefficients of the considered differential operator are not smooth enough, such an approach may fail. (ii) An alternative is provided by a test-function based strategy, that provides the decay of some integral quantities related to truncations of the solution, that in turn is connected with its regularity. (iii) Combining this idea with Steiner symmetrization, one can obtain pointwise estimates on the decreasing rearrangement of both the solution and its gradient. As a by-product of these estimates one can obtain sharp results for the summability of the solution in Lorentz spaces and more in general in rearrangement invariant spaces. In the course we will recall some classical results connected to (i) for the Poisson equation, apply the strategies outlined in (ii) and (iii) to a large class of equations in divergence form and merely measurable coefficients, and finally try to generalise the obtained results for nonlocal operators.