Around the beginning of the 20th century, classical physics, based on Newtonian Mechanics and Maxwell's equations of Electricity and Magnetism described nature as we knew it. Statistical Mechanics was also a well developed discipline describing systems with a large number of degrees of freedom. Around that time, Einstein introduced Special Relativity which was compatible with Maxwell's equations but changed our understanding of space-time and modified Mechanics.
Many things remained unexplained.
While the electron as a constituent of atoms had been found,
atomic structure was rich and quite mysterious.
problems with classical physics,
including Black Body Radiation, the Photoelectric effect, basic Atomic Theory,
Compton Scattering, and eventually with the diffraction of all kinds of particles.
Plank hypothesized that EM energy was always emitted in quanta
Jim Branson 2013-04-22