We reviewed the single-molecule science based on single-molecule measurements using tunneling current and ionic current as probes. Single-molecule measurements using tunneling currents can determine the number of molecules connected to a nanogap electrode. In addition, single-molecule measurements enable measuring the molecular vibration, local temperature, thermoelectric power, and electrode-molecule binding energy of a single molecule connected between electrodes. In addition, as a physical quantity, the phase information of the frontier molecular orbital of single molecules is measured. On the other hand, using an ionic current, single-molecule measurements enable highly accurate identification of a bacterium or virus that passes through a nanopore having a through-hole with a diameter of several μm or less. Nanopores are also a stage for elucidating the flow dynamics of a single substance transported in a liquid confined in a nanospace. Single-molecule science, which is growing as a fundamental discipline, is advancing to applied research targeting biomolecules. Furthermore, the fusion of single-molecule measurements and artificial intelligence will enable data analysis methods that are different from conventional ones. It is also becoming possible to investigate the properties of a single molecule rather than the statistical average molecular behavior.