Renormalization of pinned elastic systems: how does it work beyond one loop ?

We study the field theories for pinned elastic systems at equilibrium and at depinning. Their $\beta$-functions differ to two loops by novel ``anomalous’’ terms. At equilibrium we find a roughness $\zeta=0.20829804 \epsilon + 0.006858 \epsilon^2$(randombond),$\zeta=\epsilon/3$ (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find $\zeta =\frac{ϵ}{3}(1+0.14331ϵ)$, $ϵ=4-d$, in violation of the conjecture $\zeta =ϵ\mathrm{/}3$, solving the discrepancy with simulations. For long range elasticity $\zeta =\frac{ϵ}{3}(1+0.39735ϵ)$, $ϵ=2-d$, much closer to the experimental value ($\approx 0.5$ both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.