A current measurement apparatus includes a shunt resistor (1) located between two terminal members (5, 6), each connected electrically to a respective end (4, 3) of the shunt resistor, and each extending over substantially the whole of an adjacent side face of the shunt resistor. Electrically insulating, thermally conductive material (8, 9) is provided between each side face of the shunt resistor (1) and the terminal members (5, 6), and serves to provide a thermal path for heat exchange between the shunt resistor and the terminals. The shunt resistor (1) is engineered to have the desired electrical properties, and the terminal members are connected by mechanical fasteners (13, 14) to ensure the required electrical properties without calibration. Measuring circuitry (15) is incorporated between the shunt resistor (1) and terminal members (5, 6). The invention is implemented as a compact assembly encased in an outer insulated housing (18, 19) and is conveniently connectable to a battery terminal, to monitor current flow.