## 1 Introduction  
Food waste (FW), a major fraction of municipal solid waste (37-62%), is complex, produced in large amounts, and perishable [1, 2]. Globally, urbanization coupled with an increasing population has triggered the rapid generation of FW, reaching 1.3 billion tons annually [3]. This is a multifaceted issue due to FW's dual properties of being both a resource and a hazard [4]. FW can cause water quality deterioration and land pollution and can emit offensive colors [5]. With the increasing amount of FW, proper management strategies require clean recycling technologies. Currently, FW management is performed through landfill, fertilizer generation, composing, incination, and anaerobic digestion [4, 6]. Anaerobic digestion, a biochemical process that converts organic matter into renewable bioenergy (methane and hydrogen), is the most straightforward and feasible technology for FW disposal [7, 8]. Volatile fatty acid (VFA) inhibition, rapid acidification, and low essential trace elements (Fe, Ni, Co, and Mo) set up a barrier for biogas generation from mono-digestion of FW [8, 9]. To tackle this challenge, anaerobic co-digestion of FW with other substrates such as sludge [10], garden waste [11], paper waste [12], and animal manure [12] have been extensively investigated. Aiming to simultaneously improve local sustainability and reduce transport costs, anaerobic co-digestion seems to be an excellent alternative when co-feedstocks are generated on-site or nearby. Microalgae (MA) are photoautotrophs that convert sunlight to chemical energy. They are characterized by a high concentration of organic matter and high productivity [13]. The excessive growth of MA in lakes has negative effects on aquatic ecosystems and even threatens the safety of drinking water [14]. Every day, thousands of tons of MA are harvested from Lake Taihu in China [15]. Further disposal of undesirable MA is urgent to avoid serious secondary pollution. Proteins, lipids, and carbohydrates are the main components of MA [16], making it a promising raw material for anaerobic digestion. MA production does not require fresh water resources or arable land and, therefore, has low levels of competition with the food market compared to other solid substrates [17]; however, mono-digestion of MA is hindered by low C/N ratios and cell wall degradability [18]. To address these obstacles, several studies have evaluated the feasibility of coupling MA with a variety of complex organic substrates, including diatomite [8], agri-industrial waste [19], and lipid waste [20]. Anaerobic co-digestion of MA could simultaneously enhance biogas production and microcystin biodegradation [21]. Because of this, co-digestion with other substrates has become an alternative strategy to recover bioenergy from MA more efficiently. Recently, the combined use of FW and MA has become a new research field. The viability of anaerobic co-digestion FW with MA has been shown [22; 23], and previous studies have demonstrated that FW mixed with diverse algae species (_Chlorella_ sp. [24], _Spirulina platensis_[25], and _Dictyosphaerium_ sp. [26]) facilitated the increased performance of anaerobic co-digestion for biogas production. The co-digestion of FW and MA has multiple advantages, including the ability to improve biodegradability, dilute toxic compounds, alleviate nutrient imbalances, maintain system stability, and enhance microbial synergistic effects [18]. Furthermore, the co-digestion effluent produced is rich in phosphorus and nitrogen and could be recycled and used as a nutrient source for MA farming [25], treating the waste stream as well as reducing cultivation costs. Although previous studies demonstrated some positive results for the co-disposal of FW and MA, the current knowledge in this field is far from complete [26]. Aside from optimizing operating parameters such as the mixing ratio, the synergistic effect and kinetics of biogas evolution as regulated by the heterogeneity of FW and MA need to be further studied.