The colonization of land by plants shaped the terrestrial biosphere, the geosphere and global climates. The nature of morphological and molecular innovation driving land plant evolution has been an enigma for over 200 years. Recent phylogenetic and palaeobotanical advances jointly demonstrate that land plants evolved from freshwater algae and pinpoint key morphological innovations in plant evolution. In the haploid gametophyte phase of the plant life cycle, these include the innovation of mulitcellular forms with apical growth and multiple growth axes. In the diploid phase of the life cycle, multicellular axial sporophytes were an early innovation priming subsequent diversification of indeterminate branched forms with leaves and roots. Reverse and forward genetic approaches in newly emerging model systems are starting to identify the genetic basis of such innovations. The data place plant evo-devo research at the cusp of discovering the developmental and genetic changes driving the radiation of land plant body plans. This article is part of the themed issue 'Evo-devo in the genomics era, and the origins of morphological diversity'.