Apollo 11 astronaut Buzz Aldrin told Tech Insider that we'll need at least 25 years and cooperation between three rival nations to make it happen. Musk, meanwhile, has said he expects to do it in 11 or 12 years.
That sounds ambitious because it is.
On Friday, April 8, however, Musk's own vision for humanity crept significantly closer to reality.
SpaceX, the tech billionaire's aerospace company, landed part of a rocket on a wobbly ship at sea — the first such feat in human history.
Not to miss the historic moment, US President Barack Obama took to Twitter to congratulate the company:
—President Obama (@POTUS) April 8, 2016
Now, perhaps riding that success, Musk said Friday that his detailed plans for Mars domination will go public this fall, according to Chris Welch of the Verge:
—Chris Welch (@chriswelch) April 8, 2016
It's a big deal that SpaceX has proven its self-landing rocket scheme can work. The feat could soon lead to dramatic reductions in the cost of access to space.
A recyclable rocket is just part of the equation, though. SpaceX is also developing a whole suite of spacecraft destined for the Red Planet.
For example, models of its Dragon space capsule — a vessel designed specifically for shuttling cargo and eventually astronauts to the International Space Station — have enjoyed a round of successful tests in the past few years.
But if Musk has his way, a more advanced model, called Red Dragon, will eventually carry the first humans to Mars.
We're not sure what Musk's full plans are, and we may have to wait until September 2016 to see them.
Until then, you can peruse a storm of Instagram posts that Musk published in September 2015. They highlight a few illustrations of Red Dragon and what it would look like landing on Mars.
After traveling millions of miles, the Red Dragon would finally enter Mars' orbit.
Then it would plunge into the Red Planet's atmosphere, traveling so fast that it will need to withstand temperatures of around 3,800 degrees Fahrenheit.
Once it nears the surface of the planet, Red Dragon would fire its supersonic thrusters to line itself up for the landing.
The capsule would then touch down on Mars.
And the humans inside would step out onto Martian soil.
SpaceX has already successfully tested Dragon and Dragon 2. The Red Dragon could be on its way sooner than we think.
Musk is certainly optimistic. He thinks we'll see the first humans on Mars in 11 or 12 years.
Kelly Dickerson contributed to this post.