Triboelectric nanogenerator (TENG) harvesting living environmental energy has been demonstrated to be a potential energy source for internet of things, for its unique properties, such as high-output performance, clean, sustainability, low-cost etc., which have resulted in an explosive growth of related research in the past several years. However, due to the unique features of electrical output signals of TENGs like the pulsed output with random amplitude and frequency, ultra-high voltages and impedance, the electrical power generated by TENGs is hard to be delivered to the load efficiently or stored directly by the classical power management methods. Meanwhile, the mechanical energy from the environment is time dependent, unstable and sometime unpredictable, but the power required to drive electronics is regulated with a fixed input voltage and power. So it is important to store the generated energy in a battery or capacitor, so that it can be used to power a device sustainably. Fortunately, both the power management and energy storage for TENG have obtained significantly progress recently. Here, this paper reviews the progress made in power management and storage, including theoretical development, charge boosting, buck converting, energy storage, and the new enabled applications, aiming at building a self-charging power unit (SCPU) that can be a standard power package for sustainable operation of an electronic device. Finally, we will give an outlook for future development of applying SCPU for internet of things.