The transition to a renewable electricity system implies a larger share of power production from wind and solar energy, and this share is increasing. The intermittent nature of these energy sources stresses a challenge when sustaining the balance between power supply and demand. Solutions to balance the electricity system are to introducing flexible supply of renewable electricity, different energy storages, and demand-side flexibility. Anaerobic digestion (AD) of organic waste in biogas plants serves as a circular waste handling technique that converts waste into biomethane and biofertilizers. Flexible operation of biogas plants is a promising option to produce electricity on demand and compensate for the fluctuations in wind and solar energy. This strategy combines two important components of sustainable development: circularity related to biogas and biofertilizers produced from organic waste and increased flexibility in the electricity network which facilitate an increased share of renewable electricity production. This paper reviews research about flexible operations of biogas plants to support the electricity system. The study aims to provide an overview of different options for demand-oriented power production from biogas. The review identified four main options for flexible supply of biogas: Technical flexibility by increasing the biogas storage and electricity production capacities. Stored biogas can be used to produce electricity on demand; Technical flexibility by combining biogas upgrading to biomethane with CHP production, where there is a flexibility in choosing to produce electricity and heat or send the biogas to upgrading facility; Bio-technical flexibility by combining AD and power-to-hydrogen. In a methanation reaction, carbon dioxide from the AD and hydrogen from the electrolysis forms methane; 4) Biological flexibility by introducing flexible feeding of the AD to increase or decrease the biogas production on demand.