If there is no ceiling or other obstacle in their way, balloons ascend higher and higher until they are out of view, but how high can balloons actually fly? Helium-filled balloons can reach several miles above the Earth's surface, but they cannot float into space (if they could, that'd just mean more space junk we'd have to deal with).
According to Robert Matthews of Science Focus, toy balloons can ascend around six miles high, while weather balloons (which are made of more durable materials) can go three times that distance. This is thanks to the Archimedes Principle (explained here in this Carol Hodanbosi article for NASA). The balloon floats in the first place because its helium is less dense than the air outside. As a balloon climbs higher, the surrounding air pressure drops, and the helium inside expands. When the density of the balloon matches the density of the air, its ascension stops. And when the expanding helium becomes too much for the toy balloon's latex material, it bursts.