The discovery of traces of life in the ancient Mars meteorite triggered the development of the rapidly emerging field of Astrobiology. Astrobiologists are seeking to develop conclusive methods to recognize biosignatures and microfossils of bacteria and other microbiota as well as to understand the spatial, temporal, environmental and chemical limitations of microbial extremophiles. Recent discoveries have revealed the great distribution and diversity of microbial extremophiles on Earth and profoundly increased the probability that life may exist elsewhere in the Cosmos. The rapidly emerging science of Bacterial Paleontology has provided important new information critical to the recognition of fossil bacteria on Earth and in Astromaterials. We have recently conducted independent scanning electron microscopy and x-ray analysis investigations in the US and Russia in order to better understand the morphology and chemical composition of microfossils in ancient terrestrial rocks and carbonaceous meteorites. In this paper, we review some aspects of microbial extremophiles of Earth as modals for life on other bodies of the Solar System. We consider several of the important chemical, mineral and morphological biomarkers that provide definitive evidence of biogenic activity in ancient rocks and meteorites. We present Environmental Scanning Electron Microscope images of microfossils found in-situ in freshly fractured meteorite surfaces and describe Energy Dispersive Spectroscopy and Link microprobe analysis of the chemical elements in the mineralized and/or kerogenous microfossils and meteorite rock matrix. We also discuss technqiues and methods that may be used to help discriminate indigenous microfosils from recent terrestrial contaminants. We will also present new data from our in-situ investigations of living cyanobacteria and bacteria and freshly broken surfaces of terrestrial rocks and meteorites. Comparative analysis of these images are interpreted as providing dramatic evidence of indigenous microfossils of magnetotactic bacteria, cyanobacteria, and acritarchs in the Nogoya, Efremovka, Orgueil, Murchison and Tagish Lake Meteorites. Many of the forms in carbonaceous meteorites are large and complex providing strong evidence of biogenicity. Many of the forms found in carbonaceous meteorites are strikingly similar to microfossils of bacteria, cyanobacteria and fungi we know from the Cambrian phosphorites of Khubsugul, Mongolia and high carbon Phanerozoic and Precambrian rocks of the Siberian and Russian Platforms. Some meteorite microfossil assemblages are consistent with known characteristics of distinct microbial life cycles and reproductive stages of Nostocacean cyanobacteria. We also recognize assemblages consistent with microbial ecosystems we studied in permafrost and cryoconite communities of Antarctica, Alaska and Siberia and microfossil ecosystems from the Cambrian of Mongolia.