It is a general fact that the coupling constant of an interacting many-body Hamiltonian does not correspond to any observable and one has to infer its value by an indirect measurement. In this talk we address quantum critical systems as a resource for quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameter. In particular, if L denotes the size of a system and g is the relevant parameter driving a quantum phase transition, a precision improvement of order 1/L may be achieved in the estimation of g at the critical point compared to the noncritical case. We also show that analog results hold for temperature estimation in classical phase transitions. For the paradigmatic example of the quantum Ising model we derive the optimal quantum estimator varying size and temperature and find the optimal external field, which maximizes the quantum Fisher information, both for few spins and in the thermodynamic limit. We also show that the measurement of the total magnetization provides optimal estimation for couplings larger than a threshold value, which itself decreases with temperature.