Various methods of measuring small currents and voltages with particular reference to the theoretical and practical limits of such measurements are discussed. Most of the methods described employ thermionic valves to amplify the signals to a level suitable for indication on a robust instrument. The more important methods of converting the signal into a modulation of a carrier frequency are described, as also are the basic principles of each type of amplifier, but no attempt has been made to discuss details of circuit arrangements.Limitations of sensitivity and frequency response of each method are discussed and the precautions necessary to obtain the best sensitivity are mentioned. It is shown that a contact modulator and a capacitance modulator can be used to measure a voltage from a low-resistance source and a current from a high-resistance source, respectively, almost to the theoretical limit of random fluctuations. A direct-coupled amplifier with a contact modulator to correct for zero drifts is the best available system for a source of medium resistance when a frequency response of a few kilocycles per second is required.