The coacervates of the Poly (2-acrylamido-2-methyl-1-propanesulfonic acid-co-acrylonitrile) / β-Galactosidase complex are characterized using several techniques (Turbidimetry, dynamic and static light scattering (DLS / SLS), optical microscopy, image dynamic light scattering (IDLS), and ultra-small angles light scattering (USALS)). Turbidity and SLS were used to accurately determine the critical pHs of complex formation (pHc, pHϕ1, pHopt, and pHϕ2), DLS was used to probe the microscopic structure of coacervate droplets rich in proteins and polyelectrolytes in liquid-liquid phase separation, and IDLS and USALS have been introduced to better understand, during aging, the topology of the network formed of materials based on fractals in the dense phase. Observations of the architecture, the spatial inhomogeneity, and the size distributions of liquid complex coacervate droplets and fractal solid precipitates, were performed by optical microscopy. The pair-distance distribution function, P(r), presented in this review, is a new methodology of calculus for determining with precision the radius of gyration Rg of droplets coacervates. These techniques show that aging improves the stability of swollen condensates, the growth of the coacervate droplets is due to the attractive electrostatic interactions within the complex and does not undergo Ostwald ripening, except for the case of pHopt and having fractal dimensions Df generated by diffusion-limited cluster aggregation (DLCA).