In this talk, we explore the asymptotic behavior of sphere-valued Sobolev maps as their p-energy approaches the critical Sobolev exponent (i.e., the codimension of their singular set). Based on recent work jointly with Mattia Freguglia and Nicola Picenni, we show compactness and Gamma-convergence of the (renormalized) p-energy to the area functional of the suitable dimension. As a corollary, we also recover a classical result by Hardt and Lin on the convergence of the energy densities of p-energy minimizing maps with fixed boundary conditions, as p approaches the critical exponent. Our result establishes the analog for the p-energy of a celebrated work by Alberti, Baldo, and Orlandi for the Ginzburg-Landau energy in general dimension and codimension.