The jet shape is the fraction of the jet transverse momentum within a cone $r$ centered on the jet axis. I will present a calculation of the jet shape at next-to-leading logarithmic accuracy plus next-to-leading order (NLL$'$), accounting for logarithms of both the jet radius $R$ and the ratio $r/R$. This is the first phenomenological study that takes the recoil of the jet axis due to soft radiation into account, which is needed to reach this accuracy. This recoil complicates the calculation of collinear radiation and requires the treatment of rapidity logarithms and non-global logarithms. I will present numerical results, finding good agreement with ATLAS and CMS measurements of the jet shape in an inclusive jet sample, pp$\to$jet+X, for different kinematic bins. The effect of the underlying event and hadronization are included using a simple one-parameter model, since they are not part of our perturbative calculation.