We study the formation and structure of stable electrostatic complexes between polyanions(DNA and poly(styrene-sulfonate)) and linear polyethylenimine. The charge ratio x of the mixture istuned by varying the concentration of the polycation at constant concentration of polyanion. In agreementwith recent theories, dynamic light scattering and electrophoretic mobility measurements show two distinctregimes of weak and strong complexation. At low polycation concentration, negatively charged small complexesinvolving a few polyanion chains are observed first. By further increasing x, these small complexescondense at a precise charge ratio xc < 1 to form large anionic aggregates. The inversion of the chargeof the condensed complexes coincides with the maximum of complexation and precedes the dissolutionof the aggregates which occurs at a well-defined decondensation threshold xd > 1. Above xd, positivelycharged complexes containing again a few overcharged polyanion chains are observed. The macroscopicphase diagram is qualitatively well corroborated by AFM observation of the complexes. The influence ofentropic effects is probed by varying parameters like concentration, polycation molecular weight and ionicstrength. Structure of stable negatively charged complexes is investigated at higher concentration usingSmall Angle Neutron Scattering. In the condensed regime, we observe large soluble bundles with sharpinterfaces where the local structure of the polyanions is preserved.