Mermaids can breathe underwater, but this seems biologically dubious given that they don't show any sign of gills; the half of their body where breathing organs are normally found is the half that's humanlike, not fishlike.
It's also unclear whether they bear live young or lay eggs. Their sex organs are apparently in the fishlike half of their body, which encourages theories of egg-laying reproduction, but they also have well-developed mammaries.
Reproduction, however, presumably requires their species to have male members, but the literature has a curious scarcity of references to mermen in contrast to the more numerous females. Perhaps only the mermaids come regularly to the surface, while the men stay at home underwater as house-husbands of their more active mermaid wives.