First a few definitions I use.
Extraterrestrial life - any life outside Earth. Could also be within our solar system
Aliens - intelligent species from outside Earth


There are ~100 trillion (a million times 100 millions) stars in observable universe. Observable is a sphere of ~13.8 billion light year radius, entire universe is a bit under 50 billion light years. Assuming amount of stars is uniform that means ~10^24 stars or 1,000,000*1,000,000*1,000,000*1,000,000 stars. We seem to be finding quite a lot of extrasolar planets, many of which are in the Goldilocks zone. It would be really arrogant to assume we are the only ones around.

Now, as I said, universe is huge. It's bigger than you can possibly imagine. That means distances are similarly huge. To cover big distances one needs to either spend an eternity or do some really funky stuff with spacetime that we would most definitely notice if they happened anywhere near our solar system. This is why I'm almost certain aliens haven't visited us.

Other life forms existing outside Earth but within our solar system is actually quite likely. There are theories with quite a bit of merit to them that say life started on Mars and travelled to Earth via meteorites when it was still a simple single-celled stage. Though today mars is not really a nice place to live. Some moons around outer solar system planets are possibly habitable due to internal heat sources and having liquid water/methane. Though it's again extremely unlikely they have had the time to evolve into intelligent species. Actually finding anything multicellular outside Earth but within our solar system would be extremely unlikely.


As you can see from my bio I'm a hobbyist cosmologist/physicist so I'm very interested in the subject and would like to think I also know quite a bit about it. If you have any questions, feel free to ask.