During the past decade, synthetic nucleobase oligomers have found wide use in biochemical sciences, biotechnology and molecular medicine, both as research and/or diagnostic tools and as therapeutics. Numerous applications of common and modified oligonucleotides and oligonucleotide mimics rely on their ability to sequence-specifically recognize nucleic acid targets (DNA or RNA) by forming duplexes or triplexes. In general, these applications would benefit significantly from enhanced binding affinities of nucleobase oligomers in the formation of various secondary structures. However, for high-affinity probes, the selectivity of sequence recognition must also be improved to avoid undesirable associations with mismatched DNA and RNA sites. Here, we review recent progress in understanding the molecular mechanisms of nucleic acid interactions and the development of new high-affinity plus high-specificity oligonucleotides and their mimics, with particular emphasis on peptide nucleic acids.