Lattice QCD at finite density: imaginary chemical potential

I describe the results for the critical line and the thermodynamics of different phases of QCD which have been obtained by lattice simulations with an imaginary chemical potential. I review motivations and merits of the different strategies – Taylor expansion, Fourier analysis and Pade’ approximants – for analytic continuation from imaginary to real chemical potential. I consider phenomenological models which can be easily extended to the complex chemical potential plane, thus affording a direct comparison with lattice data at imaginary μ : the hadronic phase and the high temperature limit are amenable to a simple description, while a rather subtle interplay between thermodynamics and critical behaviour emerges in the hot phase close to Tc.