I describe the imprint which primordial magnetic fields can leave on the cosmic microwave background (CMB). I show that these are observable only if the field amplitude is of the order of View the MathML source on Mpc scale. I further argue that such fields are strongly constrained by the stochastic background of gravity waves which they produce. Primordial magnetic fields, which are strong enough to be seen in the CMB, are compatible with the nucleosynthesis bound, only if their spectrum is close to scale invariant, or maybe if helical magnetic fields provoke an inverse cascade. For helical fields, the CMB signature is especially interesting. It contains parity violating T–B and E–B correlations.