Chemical rockets operate on essentially the same technology that we've had since the 1930s, and it's dangerous, expensive, and very inefficient. It's high time for a better way of getting to space, and lasers might be the way to do it.
The problem with chemically powered rockets is that they effectively waste a crazy amount of their thrust just lifting all the fuel they need to create that thrust in the first place. Take the famous Saturn V moon rocket, for example. It weighed like 6.7 million pounds, and of that, only 250,000 pounds actually made it into low-Earth orbit. That's like 5% of the total mass of the vehicle, which in an absolute sense, is not very good.
One way around this might be to send energy to a rocket in-flight using an array of powerful microwave lasers that stay on the ground. While the lasers wouldn't power the rocket directly, they'd heat it up, and the rocket would have a propellant that would effectively convert that heat into thrust by boiling something. Specifically, a heat exchanger on the outside of the rocket would take all the heat provided by incoming laser beams and transfer it back to the engines, which would use it to turn cold liquid hydrogen into hot gaseous hydrogen and fire it out the tailpipe, and boom, you've got a rocket.
Since much of the actual reaction energy in a system like this would be coming directly from the ground and wouldn't have to be carried along, the amount of payload that a laser-powered rocket could lift would be double that of a conventional chemical rocket, or more. Also, since the propellant isn't actually exploding, the rocket would be much safer, and by shutting down the lasers on the ground, you could just turn it off if you had to.
The company trying to make this happen is called LaserMotive, and they've already proven that it's possible to use lasers to beam usable amounts of power significant distances. They envision giant arrays of ground-based lasers that could put cheap spacecraft into orbit in under five minutes, and if they can find themselves a trillion-watt laser (which might be realistic in 50 years), they'll be able to start launching laser-powered interstellar probes.