The present paper is a contribution to the taxonomy of the genus Strandesia. Here, we describe three new species: S. thomazi nov. sp., S. galeati nov. sp. and S. nakatanii nov. sp. We also describe the male of Strandesia obtusata (Sars, 1901); this is the first record of sexual populations of a Brazilian Strandesia species. Nine other Strandesia species from the Amazon, Araguaia, Pantanal and Paraná river floodplains are redescribed. We also propose that Strandesia trichosa Roessler, 1990 is a synonym of Strandesia psittacea Sars, 1901. Most of the species analyzed here are endemic to the Neotropical region, with the exception of Strandesia bicuspis (Claus, 1892) G.W. Müller, which occurs also (as an alien invasive species) in the Palaearctic. This genus occurs in water bodies with a wide range of abiotic variables and in many different aquatic macrophyte species. The species analyzed here have a highly conservative soft part morphology, but an impressive variety of carapace shapes.