Astrobiologists know about as much as the reader does on the odds of there being life outside of Earth. Although many of us secretly hope that we are not alone in this vast universe, in fact we just do not know.
To date no life has ever been found outside of Earth. We have of course managed to search for life in very few places, and arguably not very well at that. There are some reasonable claims that if we ever do find extraterrestrial life it is likely to take the form of simple microbes. This is because we argue that baby must crawl before it skips, or likewise that an organism must be single-celled before it can be complex enough to talk, walk and build space ships to travel to the Moon.
As for the Moon, this next door neighbor seems a nonideal place to find life. There is little evidence that water ever graced its potmarked surface or that an atmosphere could have been maintained at any reasonable level. We are quite confident that Mars, on the other hand, did at one point have running water on its surface.
Our best guess is that water stopping flowing on the Martian surface about 1 billion years ago. As life on Earth has been around for more than 1 billion years, one can imagine that perhaps there _was_ life on Mars which left behind microfossils just waiting to be discovered.
We are not yet able to set up a lab on Mars to make the search. As a kind of consolation prize, we are able to scrutinize Martian rock that has landed here on Earth. We can touch and analyze this rock right now. Fine, and what would we look for?
As a starting point, in a recent article on the BBC a point is made that there are some special molecules that can survive for hundreds of millions of years and which are only found associated with living organisms. One example of such a biomarker is the molecule melanin. This hardy molecule resides in our skin, dutifully protecting skin and giving us suntans. Melanin is also found in desiccated dinosaur fossils containing skin fragments.
There are efforts afoot to search for melanin and other biomarkers in tiny millimeter-sized Martian rock fragments. It’s hard work, and with a rather significant reward.