The Lemnaceae (duckweeds) are the world's smallest but fastest growing flowering plants, with a drastically reduced morphology and predominant clonal reproductive habit capable of continuous exponential growth. Here, we present assemblies of 10Lemnachromosome sets by single molecule nanopore sequencing and chromosome conformation capture. Dynamics of genome evolution in the family are revealed by syntenic comparisons withWolffiaandSpirodela, and diversification of these genera was found to coincide with the "Azolla event", in which blooms of aquatic macrophytes reduced atmospheric CO2from greenhouse levels found in the Eocene to those of the current ice age. Orthologous gene comparisons with other aquatic and terrestrial plants uncovered candidate genes for the unique metabolic and developmental features of the family, such as frequent hybrid polyploidy, lack of stomatal closure in high CO2, and accumulation of calcium oxalate, a promising candidate for carbon sequestration. Loss of a spermine-triggered gene network may account for drastic reduction in stature and preferentially adaxial stomata, a feature of floating aquatic plants. Strikingly, Lemnaceae genomes have selectively lost some of the genes required for RNA interference, including Argonaute genes required for post- zygotic reproductive isolation (the triploid block) and reduced gamete formation. Triploid hybrids arise commonly amongLemna, presumably by hybridization with unreduced gametes, and we have found mutations in highly-conserved ZMM crossover pathway genes that could support polyploid meiosis. Rapid but stable clonal propagation makesLemnaan ideal platform for continuous protein and starch micro-cropping, and for efficient sequestration of dissolved nutrients and atmospheric CO2. Facile regeneration of transgenic fronds from tissue culture, aided by reduced epigenetic silencing, makesLemnaa powerful biotechnological platform, as exemplified by recent engineering of high-oilLemnathat out-perform oil seed crops.