In 1903, Thomson suggested that atoms, and hence all matter, were composed of negative electrons embedded in positive spheres, like plums in a pudding.
However, by 1914, Rutherford realized that Thomson's model was "not worth a damn". His experiments had demonstrated conclusively that the atom had a diffuse negative cloud with a tiny positively charged core, the nucleus. He also makes the remarkably bold assertion that a new kind of neutral particle must exist in the nucleus to overcome Coulomb repulsion. His picture of the atom is essentially correct and is the crowning achievement of the atomic model of the universe -- arguably mankind's most important and pervasive paradigm of all time.
The last step in placing atomic theory in the modern age was taken by Niels Bohr in 1913 (his theory was incomplete and incorrect in some ways, but the basic ideas survive to this day).
The modern picture of atoms is firmly based on the nonrelativistic quantum theory invented by Erwin Schrödinger in 1926. This theory is capable of describing the electronic structure of the elements and all of modern chemistry.