NASA has completed the first test of an EmDrive in a vacuum chamber and confirmed that it still provides thrust. This rules out several theories about how the EmDrive works and leaves the physics of how it functions up in the air. However, it also leaves the door open for faster and cheaper space exploration in the future.
When it comes to space travel, we've barely just begun to explore the final frontier. Sure we've put men on the moon, sent probes to Mars and other planets, and we have a spacecraft (Voyager 1) leaving the solar system. But given the vast reaches of space, we're like a toddler leaving the house for the first time: we've barely reached the front porch, much less entered the yard.
There are a lot of obstacles to space travel, not least of which is that space is a very dangerous place for humans. However, an even bigger problem is one that seems simple at first: fuel. Space travel requires tons of it, literally.
At its most basic, a rocket engine is a controlled explosion with the force of the blast channeled in one direction. As Newton's third law of motion (usually paraphrased as "for every action there is an equal and opposite reaction") tells us, an explosion in one direction will drive the rocket engine, and anything attached to it, in the opposite direction.
Unfortunately, creating explosions takes fuel. Just to get the sadly retired Space Shuttle off the ground required more than 3.8 million pounds (1,900 tons) of solid and liquid fuel. Watch this jaw-dropping video if you've forgotten what that launch looks like. And that's just to get to low-Earth orbit. If you want to get to the Moon, Mars or out of the solar system, that's something else again.
Even though objects have no weight in space, they still have mass. It takes a lot of fuel to get a spacecraft to any serious level of speed, and don't forget that you need fuel to decelerate when you get to the end of your trip. The added mass of fuel for deceleration means you need more fuel for acceleration, and so on.