Nucleic acids and proteins are two major classes of biopolymers in living systems. Whereas nucleic acids are characterized by robust molecular recognition properties, essential for the reliable storage and transmission of the genetic information, the variability of structures displayed by proteins and their adaptability to the environment make them ideal functional materials. One of the major goals of DNA nanotechnology—and indeed its initial motivation—is to bridge these two worlds in a rational fashion. Combining the predictable base-pairing rule of DNA with chemical conjugation strategies and modern protein engineering methods has enabled the realization of complex DNA-protein architectures with programmable structural features and intriguing functionalities. In this review, we will focus on a special class of biohybrid structures, characterized by one or many enzyme molecules linked to a DNA scaffold with nanometer-scale precision. After an initial survey of the most important methods for coupling DNA oligomers to proteins, we will report the strategies adopted until now for organizing these conjugates in a predictable spatial arrangement. The major focus of this review will be on the consequences of such manipulations on the binding and kinetic properties of single enzymes and enzyme complexes: an interesting aspect of artificial DNA-enzyme hybrids, often reported in the literature, however, not yet entirely understood and whose full comprehension may open the way to new opportunities in protein science.