Is Life restricted to the Planet Earth? or Does life exist elsewhere in the Cosmos? The existence of extraterrestrial life is the fundamental question of Astrobiology. Detecting evidence for living organisms beyond our planet is even more difficult than finding fossilized remains of ancient organisms. Microbiological investigations during the past century have established the fundamental physical and chemical requirements and limits for life on Earth. It is now known that life requires only water, a source of energy, and a small suite of biogenic elements under a surprisingly wide range of environmental conditions. The discovery that microbial extremophiles live and grow over a very broad span of temperature, pH, salinity, pressure and radiation levels has greatly enhanced the possibility that life may be present on many bodies of our Solar System. Recent discoveries by Space Missions and Rovers have invalidated many long held paradigms regarding the distribution of water, organic chemicals and the possibility of life elsewhere in the Cosmos. This paper considers the discovery of water, ice and organics on distant planets, moons and comets and evidence for fossil organisms on Mars and in SNC and carbonaceous meteorites. Instruments and methods are considered for spectroscopy and fluorescence of biomolecules (e.g., photosynthetic pigments) for remote detection of conclusive evidence for extraterrestrial life. Optical Video Microscopy is discussed as a direct means for detecting extraterrestrial life using small visible light/UV video microscopes, with ample magnification to record motile bacteria and other living organisms in samples collected by Rovers or Landers. Locomotion of living cells of bacteria and other microbes requires great expenditure of energy and motile cells can be distinguished by video microscopy from the physico-chemical movements (by Brownian Motion, Diffusion or Current Drift) of dead cells, dust particles and abiotic mineral grains.