From Earth's surface, outer space begins at the somewhat-arbitrary Karman Line, or 100 km up, according to the Space website. From there, the observable universe stretches out without reaching any perceptible boundary.
As of 2014, the universe is 13.8 billion years old, Space reports. Given the speed of light, this places the farthest objects that can be seen from Earth as those that sit on that boundary. The universe is expanding, so objects at the extreme range of detection have since moved to a maximum distance of 48 billion light-years. Space goes on beyond that. If the universe has a flat curvature, which it very likely does, then space could be said to extend, literally, forever.