## 2 The Evolution of Aerobic Biological Systems towards the Microalgae-Bacteria Consortium  
In aerobic systems, pollutant degradation occurs mainly through microorganisms' respiration; biosynthesis and endogenous respiration can also occur [28]. It is well known that most of the BAT is implemented during domestic and industrial wastewater [29] on both small and large scales [30], and the most common aerobic technologies are aerated lagoons, biological filters, and activated sludge [28]. Nowadays, more studies are focused on process optimization, such as reducing the footprint and energy consumption [31].  
For an efficient organic matter and nitrogen removal process, a well-defined microbiota is essential, such as the presence of heterotrophic and autotrophic microorganisms, the first group of which is responsible for organic matter degradation, and the second for the initial stages of complete nitrogen removal. Ammonia-oxidizing bacteria (AOB) or ammonia-oxidizing archaea (AOA) are responsible for oxidizing ammonia to nitrite (Figure 1), which is oxidized to nitrite by nitrite-oxidizing bacteria (NOB). Subsequently, the generated nitrate is removed from the system through denitrification, where NO3\({}^{-}\) is converted to atmospheric N2 [32]. Additionally, there are two known NH4\({}^{+}\) oxidation processes:anammox, where nitrite is used as an electron acceptor under anoxic conditions and a low C/N ratio (0.2-2.5) [33,34], and comammox, a process where there is complete oxidation of ammonia to nitrate [35].  
In systems where the biomass consists of flocculent sludge, a compartment is needed to separate the treated effluent and formed sludge [36]; however, more area for construction is necessary, which leads to the technology becoming more expensive. An excellent solution is cultivating a fast-settling aggregate, such as aerobic granular sludge (AGS) [37]. Compared to activated sludge systems, aerobic granular systems can reduce construction area requirements by up to 70% and energy consumption by 40% [38, 39, 40]. Therefore, the potential for symbiosis between bacteria and algae to optimize energy utilization in aerobic systems holds promise for wastewater treatment. The formation of aggregates primarily occurs through inoculation with activated sludge [19] or is obtained from a biomass-sourced upflow anaerobic sludge blanket (UASB) [41] or from a UASB reactor biomass combined with samples from eutrophied environments [38].  
In recent years, an improvement on AGS has been studied. Since the 1970s, integrating microalgae into treatment systems has aimed to curb greenhouse gas emissions and supplant artificial aeration [11]. This approach has yielded commendable outcomes in nutrient and organic matter removal. Moreover, adoption of this approach yields biomass rich in intracellular lipids, fostering the production of value-added products [42, 43, 44]. The cultivation of microalgae and promoting the bacteria-algae consortium shows significant advantages, mostly in terms of improving the sludge sedimentation, the final effluent quality, the gas exchange, and the granular stability. Although previous studies have explored aggregates of microalgae and bacteria [45], a patent for the algal granulation process was issued based on the work of [PERSON] and [PERSON] (2015) [46], who observed the formation of these structures through inoculation with activated sludge and microalgae. The operational strategies and characteristics of microalgae-bacteria is discussed is the following chapters.