  The jet shape is the fraction of the jet energy within a cone $r$ centered on
the jet axis. We calculate the jet shape distribution 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, but complicates
the calculation of collinear radiation and requires the treatment of rapidity
logarithms and non-global logarithms. We present numerical results, finding
good agreement with ATLAS and CMS measurements of the jet shape in an inclusive
jet sample, $pp \to {\rm jet}+X$, 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.
