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Currently, the wave-particle duality model for light is the accepted model. From HyperPhysics:

The evidence for the description of light as waves was well established at the turn of the century when the photoelectric effect introduced firm evidence of a particle nature as well. On the other hand, the particle properties of electrons was well documented when the DeBroglie hypothesis and the subsequent experiments by Davisson and Germer established the wave nature of the electron.

What theories preceded both the the wave and particle theories of light?

HDE 226868
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The wave and the particle (or corpuscular) theories of light go back to the 17-th century and are often associated with Huygens and Newton, respectively, as their founders. What preceeded them was called geometric optics, where light consisted of rays connecting an eye to an object. There were two theories in geometric optics too. According to the emission theory rays of light came out of our eyes and "sensed" objects in a way similar to touch, Hero and Ptolemy supported this theory. According to the intromission theory it was objects that emanated the light, Aristotle and Galen favored this version. Mathematically both theories are equivalent for optical phenomena, and essentially reduce optics to geometry except where the refraction law is concerned. More historical details are given here.

The "particles" of light are photons rather than electrons, and although "wave-particle duality" is a popular way to explain their nature it is rather inaccurate, the real duality would have produced a pilot wave theory. The accepted model is quantum electrodynamics developed in late 1940-s, that describes also other forms of electromagnetism, and in the first approximation quantum mechanics. While photons do have some properties of waves and some of particles they do not have all, and they also have some properties (such as entanglement) that neither of the two has.

Conifold
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  • It's a bit misleading to say that quantum electrodynamics is due to Feynman. The key ideas originated with Pauli, Jordan, Heisenberg, and especially Dirac (plus others). The self-energy problem made it impossible to carry out certain computations. Bethe did the first important renormalization computation, Feynman, Schwinger, and Tomonaga then all developed the idea, with Feynman's formalism proving the most convenient. Finally, Dyson showed that the Schwinger and Feynman approaches were equivalent. See Schweber, QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga. – Michael Weiss Oct 29 '14 at 20:47
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    Olivier Darrigol's A History of Optics from Greek Antiquity to the Nineteeth Century has quite a bit on early theories of optics. If you have a Kindle, you can download a free sample that will get you as far as the middle ages. – Michael Weiss Oct 29 '14 at 20:56
  • Sorry, I corrected it. – Conifold Oct 30 '14 at 00:28
  • Don't forget the ether: http://scienceworld.wolfram.com/physics/Ether.html – Jeffrey Young Apr 06 '16 at 22:46