This review highlights various methods that can be used for a sensitive detection of nucleic acids without using thermal cycling procedures, as is done in PCR or LCR. Topics included are nucleic acid sequence-based amplification (NASBA), strand displacement amplification (SDA), loop-mediated amplification (LAMP), Invader assay, rolling circle amplification (RCA), signal mediated amplification of RNA technology (SMART), helicase-dependent amplification (HDA), recombinase polymerase amplification (RPA), nicking endonuclease signal amplification (NESA) and nicking endonuclease assisted nanoparticle activation (NENNA), exonuclease-aided target recycling, Junction or Y-probes, split DNAZyme and deoxyribozyme amplification strategies, template-directed chemical reactions that lead to amplified signals, non-covalent DNA catalytic reactions, hybridization chain reactions (HCR) and detection via the self-assembly of DNA probes to give supramolecular structures. The majority of these isothermal amplification methods can detect DNA or RNA in complex biological matrices and have great potential for use at point-of-care.