Forty-five years ago today, the world watched as astronauts Neil Armstrong and Buzz Aldrin took "one small step for man, one giant leap for mankind," becoming the first humans to walk on the moon on July 20, 1969.

The historic Apollo 11 landing established the U.S. as the leader in the Space Race against the Soviet Union, a key victory at the height of the Cold War. Today, in contrast, with the retirement of the Space Shuttle program, NASA has to pay for space aboard Russian rockets to ferry astronauts to and from the International Space Station.

Political tensions between the two countries threaten this arrangement. The U.S. has taken an increasingly hard stance against Russia's activity in Ukraine by imposing sanctions against various Russian companies and individuals. Russian officials have in turn indicated that they will not offer assistance in U.S. space endeavors.

"We're in a hostage situation," former NASA administrator Michael Griffin told ABC News. "Russia can decide that no more U.S. astronauts will launch to the International Space Station and that's not a position that I want our nation to be in."

But there is a new sort of space race happening now to help reestablish U.S. autonomy. Three private companies - Boeing, Space-Ex and Sierra Nevada - are currently competing for billions of dollars in NASA funding to build the next ride to space for American astronauts.

SLIDESHOW: Apollo 11 Anniversary

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NASA hopes to announce the winner of the competition this summer and to launch the craft based on the winning design by 2017. This is encouraging news to Aldrin, who would like to see Americans return to the moon and go beyond it.

"We don't have to repeat what we did 45 years ago, but we don't ignore the moon. It's very important for technology, commerce, science," said Aldrin.

Aldrin's historic mission inspired other astronauts to explore the cosmos. Astronaut Catherine Coleman is one of them.

"Forty-five years ago, humanity's first steps on the moon taught us what we as a society can accomplish for all mankind when we focus on a common goal," Coleman said. "Living on the space station, landing on an asteroid, eventually sending humans to Mars. We are meant to explore our universe."

Discussion of space flight has focused recently on private industry - the potential for tourism and mining, for example, as opposed to manned space exploration for its own sake. Astronauts like Coleman feel such exploration is a worthwhile expense, and a noble national goal.

"It's time for our next 'great leap,'" she said.

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