We will describe the Signorini, or lower-dimensional obstacle problem, for a uniformly elliptic, divergence form operator L = div(A(x)nabla) with Lipschitz continuous coefficients. We will give an overview of this problem and discuss some recent developments, including the optimal regularity of the solution and the $C^{1,alpha}$ regularity of the regular part of the free boundary. These are obtained by proving a new monotonicity formula for a generalization of the celebrated Almgren’s frequency functional, a new Weiss type monotonicity formula and an appropriate version of the epiperimetric inequality. This is joint work with Nicola Garofalo and Arshak Petrosyan.