•Induction of lipid biosynthesis in microalgae is reviewed.•Comprehensive strategies of strain improvement for lipid production are summarized.•Targets for enhancing lipid productivity in microalgae are suggested.•Challenges and perspectives of strain development for lipid production are discussed. Over the past decade, the number of original articles and reviews presenting microalgae as a promising feedstock for biodiesel has increased tremendously. Many improvements of microalgae have been achieved through selection and strain development for industrial applications. However, the large-scale production of lipids for commercialization is not yet realistic because the production is still much more expensive than that of agricultural products. This review summarizes recent research on the induction of lipid biosynthesis in microalgae and the various strategies of genetic and metabolic engineering for enhancing lipid production. Strain engineering targets are proposed based on these strategies. To address current limitations of strain engineering for lipid production, this review provides insights on recent engineering strategies based on molecular tools and methods, and also discusses further perspectives.