The enigma of symbiotic objects began to unfold when IUE opened the 1200 Å - 3200 Å spectral range. They turned out to be intrinsically binary, consisting of a red giant and a very hot and small secondary star, often a white dwarf. The relative elemental abundances showed that the nebula was due to mass-loss by the red giant. The radio spectra were compatible with a nebula consisting of a fractionally ionized stellar wind which was attributed to the red giant. These findings led to the first calculated radiative ionization models for symbiotic objects. Discrepancies between observed and model flux ratios of nebular emission lines, and emission line profiles led to the conclusion that in some symbiotics the hot star was losing mass as well. The ionization models therefore had to be extended to include the existence of two stellar winds. This called for a proper hydrodynamic treatment of the wind-wind collision and the resulting structuring of the nebular environment, and the inclusion of collisional ionization in the models. - Symbiotics contain at the same time dust of low temperature and high temperature shocked wind regions, they contain the cool spectrum of a red giant and the hot continuum of a white dwarf. We therefore need observations from X-ray to radio wavelengths. In addition, polarization studies have become an important and very promising way of deciphering the structure of symbiotic systems. Polarization studies and tomographic methods help, in particular, to find the internal boundaries between ionized and neutral regions.