Possible relic biogenic activity in martian meteorite ALH84001 was proposed by McKay et al. (Science, 273, 924-930, 1996). This ancient meteorite of 4.5 billion years old contains abundant carbonates as secondary minerals precipitated from a fluid on the martian surface. They showed the following lines of evidence for the ancient life; (1) unique mineral compositions and biominerals, (2) polycyclic aromatic hydrocarbons (PAHs) in association with the carbonates, and (3) unique structures and morphologies typical of nanobacteria or microfossils. This review is divided into two parts; one is on the martian meteorites in general and ALH84001, which has many features unlike other martian meteorites, and the other is on mineralogical (biomineralogical) and geochemical features of the carbonates and microfossil-like structures. There is little doubt that ALH84001 is from Mars as well as eleven other SNC meteorites. However, the mineralogical and biomineralogical evidence for martian bacteria given by McKay et al. (1996) is controversial, and could be formed by non-biogenic processes. Thus, further study of ALH84001 and other martian meteorites is required. We also need to consider the future Mars mission especially sample return mission.