In this review, we explore progress on DNA aptamers (evolved DNA), DNA circuits (designed DNA), and the newest projects that integrate both. Designed DNA nanotechnology includes static nanostructures, dynamic nanodevices, and reaction networks (sometimes called DNA circuits). DNA circuits are dynamic DNA reactions that perform computations and sequence-specific amplification. Directed evolution can be used to produce DNA that can recognize specific targets. Aptamers are evolved nucleic acids; they are produced artificially with an in vitro selection process. DNA aptamers are molecular recognition elements made of single-stranded DNA (ssDNA) with the potential to interact with proteins, small molecules, viruses, and even cells. Designed molecular structures can incorporate aptamers for applications with immediate practical impact.