A review of the mineralogical, isotopic, and chemical properties of the carbonates and associated submicrometer iron oxides and sulfides in Martian meteorite ALH84001 provides minimal evidence for microbial activity. Some magnetites resemble those formed by magnetotactic microorganisms but cubic crystals <50 nm in size and elongated grains <25 nm long are too small to be single-domain magnets and are probably abiogenic. Magnetites with shapes that are clearly unique to magnetotactic bacteria appear to be absent in ALH84001. Magnetosomes have not been reported in plutonic rocks and are unlikely to have been transported in fluids through fractures and uniformly deposited where abiogenic magnetite was forming epitaxially on carbonate. Submicrometer sulfides and magnetites probably formed during shock heating. Carbonates have correlated variations in Ca, Mg, and 18O/16O, magnetite-rich rims, and they appear to be embedded in pyroxene and plagioclase glass. Carbonates with these features have not been identified in carbonaceous chondrites and terrestrial rocks, suggesting that the ALH84001 carbonates have a unique origin. Carbonates and hydrated minerals in ALH84001, like secondary phases in other Martian meteorites, have O and H isotopic ratios favoring formation from fluids that exchanged with the Martian atmosphere. I propose that carbonates originally formed in ALH84001 from aqueous fluids and were subsequently shock heated and vaporized. The original carbonates were probably dolomite-magnesite-siderite assemblages that formed in pores at interstitial sites with minor sulfate, chloride, and phyllosilicates. These phases, like many other volatile-rich phases in Martian meteorites, may have formed as evaporite deposits from intermittent floods.