This chapter reviews the state-of-the-art in the study of molecular or colloidal systems whose mutual interactions are mediated by DNA molecules. In the last decade, the robust current knowledge of DNA interactions has enabled an impressive growth of self-assembled DNA-based structures that depend crucially on the properties of DNA-DNA interactions. In many cases, structures are built on design by exploiting the programmable selectivity of DNA interactions and the modularity of their strength. The study of DNA-based materials is definitely an emerging field in condensed matter physics, nanotechnology, and material science. This chapter will consider both systems that are entirely constructed by DNA and hybrid systems in which latex or metal colloidal particles are coated by DNA strands. We will confine our discussion to systems in which DNA-mediated interactions promote the formation of "phases," that is structures extending on length scales much larger than the building blocks. Their self-assembly typically involves a large number of interacting particles and often features hierarchical stages of structuring. Because of the possibility of fine-tuning the geometry and strength of the DNA-mediated interactions, these systems are characterized by a wide variety of patterns of self-assembly, ranging from amorphous, to liquid crystalline, to crystalline in one, two, or three dimensions.