We construct the field theory which describes the universal properties of the quasi-static isotropic depinning transition for interfaces and elastic periodic systems at zero temperature, taking properly into account the nonanalytic form of the dynamical action. This cures the inability of the 1-loop flow-equations to distinguish between statics and quasi-static depinning, and thus to account for the irreversibility of the latter. We prove two-loop renormalizability, obtain the 2-loop β-function and show the generation of "irreversible" anomalous terms, originating from the non-analytic nature of the theory, which cause the statics and driven dynamics to differ at 2-loop order. We obtain the roughness exponent ζ and dynamical exponent z to order ǫ 2 . This allows to test several previous conjectures made on the basis of the 1-loop result. First it demonstrates that randomfield disorder does indeed attract all disorder of shorter range. It also shows that the conjecture ζ = ǫ/3 is incorrect, and allows to compute the violations, as ζ = ǫ 3(1 + 0.14331ǫ), ǫ = 4 − d. This solves a longstanding discrepancy with simulations. For long-range elasticity it yields ζ = ǫ 3(1 + 0.39735ǫ), ǫ = 2 − d (vs. the standard prediction ζ = 1/3 for d = 1), in reasonable agreement with the most recent simulations. The high value of ζ ≈ 0.5 found in experiments both on the contact line depinning of liquid Helium and on slow crack fronts is discussed.