The theory of black holes answers scientists' questions about the life of a star after its collapse. As a star begins to die, its internal pressures decrease. When the internal pressures of a star reach a certain point, the internal gravity in a star compresses all of the star's matter into a small area in the center. This increases the overall mass in the center, which increases the gravity of the star further. As a result, the gravity at this point compresses the matter into a single point, raising the overall gravity so high that light can no longer leave.
Wormholes answer scientists questions about methods to increase speed beyond the speed of light. The idea is that you could travel through a wormhole at a single, sub light, speed, beginning your trip on one side and ending on the other. The distance between the starting point and concluding point could be substantial. While your speed would never actually reach the speed of light, the distance you could travel would be further than you could travel at light speed.
Scientists found the earliest proof of black holes by examining the activity of other solar bodies around suspected black holes. Essentially, the overall gravity of black holes is so massive that they alter things around them, such as comets, planets, moons or energy in space. Stephen Hawking gave scientists a new way to search for black holes in 1974, by explaining the process of thermal releases from black holes, called Hawking radiation. This lead to new methods for scientists to search for black holes and more evidence supports their existence.
Currently, wormholes are purely theoretical. They exist as mathematical theories and as part of some mathematical diagrams. Wormholes serve as a significant resource for science fiction, providing a basis for time travel and faster-than-light travel, and allowing characters to transverse exceptionally large areas of space. Scientists continue to look for more evidence of wormholes; however, there is no reliable physical evidence that they exist.