Extremophiles -- organisms that live in extreme environments, like hot springs or dry Antarctic valleys. (although.. the name 'extremophile' highlights our bias, as a hot spring environment can hardly be considered extreme to the organisms dwelling there.) By studying life that thrives in environments normally considered hostile, scientists have expanded our awareness of where we might find life. Extremes of temperature (both hot and cold), pressure, salinity, acidity, radiation... life on Earth can cope with a wide variety of conditions. The most extreme survivors tend to be bacteria, but tardigrades are remarkable little animals that have even survived exposure to outer space. Some extremophiles live in environments similar to what can be found in locations on Mars. This raises the possibility that if life evolved on an ancient, wetter and warmer Mars, it might still exist there, thriving in a vast ocean of subsurface ice.
Biosignatures -- What constitutes evidence of life? Before we can find proof of life on other planets, we need to know what we're looking for. Most of the life on Earth, for most of its history, has been microbial. From this, we can assume there will be more single-celled life in the universe, making detection somewhat more difficult. Even the evidence for the earliest life on Earth is still debated, because microbes don't leave obvious bones in the ground. Microfossil structures have that resemble contemporary bacteria have been found in sedimentary deposits dating back 3.5 billion years; but morphology is not a sufficient indicator of biogenicity. Processes leading to the preservation of structures on the microscopic scale are not well understood, and what looks like an ancient cyanobacteria could be an abiotic artifact. Even if Mars is dead now, it might have once harbored life. To plan future missions and prevent overstating any evidence, astrobiologists attempt to define what makes for clear indicators of past life.
The Origins of Life -- one of the greatest ponderables of all time! Science has yet to advance a complete theory regarding the origins of life on Earth. The theory of evolution covers the speciation of life once it has developed, but does not address the question of life's origins. Darwin wrote to a colleague about the possibility of life forming in a "warm little pond" initiating speculation about the primordial soup, and prebiotic chemists have since tried to recreate the recipe, without success. The most famous experiment occurred in the 1950's, when Stanley Miller was able to synthesize some of the building blocks of life, including amino acids, from simple molecular precursors. Currently, the RNA World hypothesis seems the main contender for the origins of life, positing simple life forms of ribonucleic acid, before the development of proteins and DNA (deoxyribonucleic acid). An understanding of the conditions necessary for the origins of life on Earth can help guide the search for extraterrestrial life, by predicting where the transition from chemistry to biology might also have occurred.
NASA defines astrobiology as "the study of the origins, evolution, distribution, and future of life in the universe." It is the study of the extent of life in the universe, which includes life on Earth. Indeed, the study of Earth-based life forms the foundation of how to look for alien life, even if we have yet to find any.