How do current mirrors work and what are the common topologies?

A basic current mirror uses two matched transistors; one is diode-connected (reference) and sets the current, the other mirrors this current to the output. For BJTs: Iout = Iref * (1 + 1/beta), with output impedance ro. Improved topologies include: Wilson current mirror (higher output impedance, reduced beta error), Cascode current mirror (very high output impedance for precision applications), and Widlar current mirror (for generating small currents from larger references using emitter resistor).