branching brownian motion is a prototype of a disordered system and a toy model for spin glasses and log-correlated fields. it also has an exact duality relation with the fkpp equation, a well-known reaction diffusion equation. in this talk, i will present recent results (obtained with michel pain) on the fluctuations of the gibbs measure at the critical temperature. by gibbs measure i mean here the measure whose atoms are the positions of the particles, weighted by their gibbs weight. it is known that this gibbs measure, after a suitable scaling, converges to a deterministic measure. we prove a non-standard central limit theorem for the integral of a function against the gibbs measure, for a large class of functions. the possible limits are 1-stable laws with arbitrary asymmetry parameter depending on the function. in particular, the derivative martingale and the usual additive martingale satisfy such a central limit theorem with, respectively, a totally asymmetric and a cauchy distribution.