In the early 19th century, most phenomenons can be explained by classical (or Newtonian) mechanics. By the turn of the century, however, many anomalies instances spawned that can only be explained through Relativity and Quantum Mechanics. Relativity was discovered mainly to describe physics of very massive and very fast objects. Quantum Mechanics was developed to describe the physics of very small objects.
Both Quantum Mechanics and Relativity contradict Newtonian Mechanics which make it very difficult to comprehend. However, both produce results equivalence to Newtonian results when applied to our physical world.