Storage of starch and lipids in microalgae: biosynthesis and manipulation by nutrients

•Starch biosynthesis under nutrient depletion involve starch phosphorylase and PGM.•TAG synthesis is determined by the precursor supply and glycerolipid assembly.•Nutrient manipulation achieves high storage metabolites production in microalgae.•Relieving oxidative stress of nutrient depletion improves starch/lipid production.•Storage metabolites biosynthesis and regulation need in-depth research.