Encrusting aragonitic calcareous algae of the family Peyssonneliaceae are the largest group of calcified red algae outside the well-known Mg calcite Corallinaceae. They are distributed worldwide, are most heavily calcified in temperate and tropical waters, and grow as prone but arched sheets on soft mud substrates, on hard rock surfaces, as extensive bridge-like networks between corals in reefs, and as concentric layers in nodules. Calcification is entirely aragonitic, species-specific, and both intracellular and extracellular below the thallus as a hypobasal layer. The hypobasal layer develops outside the tissue as an encrustation of small aragonite botryoids attached to the lower surface between rhyzoids, and on living plants it may exceed the thickness of the thallus. Calcification ranges from nonexistent in some cold-water forms, to thallus calcification only, to both thallus and hypobasal calcification, to species in which the thallus is noncalcified but there is a hypobasal layer of aragonite botryoids. Although the confirmed fossil range of this family extends only to the Early Cretaceous, striking similarities between these aragonitic forms and some late Paleozoic phylloid algae suggest that they may be closely related. Their ability to grow on soft mud substrates and form structures composed of irregular arched sheets with extensive pore space, as well as their brittle nature, so susceptible to fragmentation, are all characteristics of mound-forming fossil phylloid algae. The hypobasal layer of botryoidal aragonite, developed while the plant is still growing, could easily act as a nucleation site for further epitaxial submarine precipitation, thus explaining the common association of Paleozoic phylloid algae and extensive fossil-reef cements that resemble botryoidal aragonite. The presence of hypobasal botryoidal aragonite on plants with a noncalcified thallus raises the possibility that some fossil-reef cements may be related to now-vanished algae.