The thesis describes how demixing of binary colloidal mixtures could be used to design new kinds of amorphous structures. We show that a rich phase behavior emerges, dependent on density (colloidal concentration) and composition (species relative populations). A simple model is adopted for the colloidal particles, which are assumed to be hard spheres interacting via an effective short-ranged attractive square-well (SW) potential. We show that demixing - due to composition fluctuations - can strongly interfere with typically dominating condensation mechanism - due to density fluctuations,- if the inter-species attraction is significantly reduced with respect to intra-species one. Thermodynamic perturbation theory (TPT) calculations and extensive numerical simulations have been performed on binary mixtures of the SW model. In the whole range of compositions and densities, we demonstrate how the enhancement of demixing over condensation brings to distinctive properties of the arrested structures. If the population of one colloidal species largely exceeds the other (asymmetric composition), the typical condensation mechanism dominates and brings to the percolation of only the main species. Instead, demixing separation prevails approaching the symmetric composition, and results in two interpenetrating sub-gels, both percolating. We name this structure a BiGel. The formation of BiGels has been analyzed in the thesis, pointing out structural differences and similarities with the usual one-component gel. In particular, we implemented a novel method that enables an explicit topological characterization. Despite the sub-gel branches of a BiGel present longer and thinner arms, we quantified the resemblance of gels and BiGels at large length-scales in light of their congruent porosities. Furthermore, we propose an experimental exploration of the dominant demixing scenario. The possibility is offered by the fine tuning of inter-species interactions that can be achieved in DNA-coated colloids (DNACCs). Thus, the numerical investigation is complemented with experiments on symmetric mixtures of DNACCs and the proof of BiGel’s actual realization. The main result of the thesis is the demonstration that, in presence of tunable inter-particle interactions, phase separation driven by the demixing mechanism can be arrested in the same fashion as condensation. We show how to enhance the demixing and demonstrate, by simulations and experiments, the possibility of multi-component gelation. Notably, complex structures result without requiring complex architectures of the single particles, nor anisotropic potentials, as isotropic spherical colloids already constitute suitable building blocks. Hence, the results and ideas here presented may find application in the design and development of novel types of materials.