Recently, there has been a rapid progress in the development of techniques for isothermal amplification of nucleic acids as an alternative to polymerase chain reaction (PCR). The advantage of these methods is that the nucleic acids amplification can be carried out at constant temperature, unlike PCR, which requires cyclic temperature changes. Moreover, isothermal amplification can be conducted directly in living cells. This review describes the principles of isothermal amplification techniques and demonstrates their high efficiency in designing new highly sensitive detection methods of nucleic acids and enzymes involved in their modifications. The data on successful application of isothermal amplification methods for the analysis of cells and biomolecules with the use of DNA/RNA aptamers are presented.