In analogy to split-protein systems, which rely on the appropriate fragmentation of protein domains, split aptamers made of two or more short nucleic acid strands have emerged as novel tools in biosensor set-ups. The concept relies on dissecting an aptamer into a series of two or more independent fragments, able to assemble in the presence of a specific target. The stability of the assembled structure can further be enhanced by functionalities that upon folding would lead to covalent end-joining of the fragments. To date, only a few aptamers have been split successfully, and application of split aptamers in biosensing approaches remains as promising as it is challenging. Further improving the stability of split aptamer target complexes and with that the sensitivity as well as efficient working modes are important tasks. Here we review functional nucleic acid assemblies that are derived from aptamers and ribozymes/DNAzymes. We focus on the thrombin, the adenosine/ATP and the cocaine split aptamers as the three most studied DNA split systems and on split DNAzyme assemblies. Furthermore, we extend the subject into split light up RNA aptamers used as mimics of the green fluorescent protein (GFP), and split ribozymes.