As the above quote illustrates, the platypus is a bizarre beast. Belonging to the order Monotremata (literally, 'single hole'), all urinary, defecatory and reproductive systems open into a single duct, the cloaca (literally, 'sewer') and as most people know is one of the few mammals to lay eggs (the few species of echidna being the others). Platypus eggs more closely resemble those of reptiles than birds and are incubated in utero for the majority of the incubation period. The female has 2 ovaries, but only one is functional. It is also rare amongst mammals in that the male of the species has spurs on the hind legs that can produce venom toxic enough to kill a dog, or cause a great deal of pain to a human.
As if being a cross between a bird and a reptile wasn't enough, the platypus bill is packed with nerves that can be used for electrolocation, more commonly found in fish species, to aid in foraging in the riverbed.
But ultimately, the platypus is mammalian, meaning it has mammary glands, produces milk and nurses its young. Even in this aspect of its physiology, the platypus is unique. Unlike other mammals, the platypus has no nipples. Instead, the mammary glands are more like sweat glands, secreting milk directly onto the fur where it is licked off by its young.
Genetically, the platypus has other interesting features including a strange quirk in visual pigment evolution and in its sex chromosomes. The platypus has 5 pairs of sex chromosomes (making up ~15% of the genome) lacking the classic sex-determining SRY gene, which in some ways resemble the reptile/bird ZW sex determination system.
Because of its shared characteristics between mammal and reptile, some people view the platypus as an evolutionary link between the two. Because of their unique phylogenetic position, the platypus genome is currently being sequenced to answer some questions about evolutionary biology and mammalian gene organization.