In some ways the Space Shuttle is a plane that can get into space and then fly / glide back down to earth.
A UK company called Reaction Engines are trying to develop a single engine that will use air like a conventional jet engine but can then convert to rocket propulsion during flight . . . such an engine would allow you to take off from the ground horizontally (from a normal runway), build up lots of speed, fly to an altitude where the air is much thinner then, at the point where the air breathing engine stops working (because there is no air) convert to rocket mode and blast into space. The plane would be able to do it all in reverse to land. Such a capability in one engine would allow the plane to be reused over and over again making access to space much cheaper . . . with conventional single-use rockets, the cost of the rocket needs to be borne by the single launch, whereas with a re-useable system you can spread the cost over many, many missions. This is what SpaceX are trying to do with re-land-able rockets.
Maybe, some time soon, we will see planes taking off from Heathrow and landing in Sydney only 2 hours later!!