If extra-terrestrials ever landed on Earth, they would find us extremely strange. Their first intimation of our existence might well be a Super Bowl broadcast or a stray transmission from the Playboy channel. But, of course, they might seem equally strange to us. How strange? Their senses could be entirely different from ours, they might see in the infrared or hear" radio waves. What would aliens look like? An intelligent octopus-like creature is certainly plausible. What about odd numbers of limbs, a three-legged alien with three arms and three eyes? What about an entire planet of immobile, silicon-based trees" that communicate with each other via electrical signals? The Science of Aliens gets weirder still. Could a giant interstellar cloud be alive" and intelligent? Could creatures live at extremely high pressures and temperatures? And which of these many possibilities would be similar enough to us that they could communicate with them, or they with us? Would they have any interest in abducting us? Would they want to have sex with us? In classic Pickover style, here is speculation at the far edge of knowledge, and beyond.