Algae are (mostly) photosynthetic eukaryotes that occupy multiple branches of the tree of life, and are vital for planet function and health. In this review, we highlight a transformative period in studies of the evolution and functioning of this extraordinary group of organisms and their potential for novel applications, wrought by high-throughput 'omic' and reverse genetic methods. We cover the origin and diversification of algal groups, explore advances in understanding the link between phenotype and genotype, consider algal sex determination, and review progress in understanding the roots of algal multicellularity. Experimental evolution studies to determine how algae evolve in changing environments are highlighted, as is their potential as production platforms for compounds of commercial interest, such as biofuel precursors, nutraceuticals, or therapeutics.