the Standard Model
The Standard Model is the single most successful theory humans have ever written down, and also, physicists will freely admit, an unfinished one. Picture a periodic table not of elements but of the truly fundamental: twelve matter particles, a handful of force carriers, and one special field that gives mass. Everything you have ever touched, every chemical reaction, every star, is built from that short list interacting by three of the four known forces. It answers the oldest question in physics, what is the world made of and how do the pieces push on one another, with unnerving precision.
Technically the Standard Model is a relativistic quantum field theory with the gauge symmetry SU(3)_C x SU(2)_L x U(1)_Y. The SU(3) factor is the color symmetry of quantum chromodynamics (the strong force, eight gluons); the SU(2) x U(1) factor is the electroweak sector, whose symmetry is spontaneously broken by the Higgs field down to the U(1) of electromagnetism, leaving one massless photon and three massive carriers, the W+, W- and Z. The matter content is three generations of quarks and leptons, and the whole theory is fixed by about nineteen free parameters, masses, mixing angles and coupling strengths, that must be measured, not derived.
The model's predictions, from the anomalous magnetic moment of the electron to the very existence and mass pattern of the W, Z and Higgs bosons, have survived every accelerator test for fifty years, capped by the 2012 discovery of the Higgs boson at the LHC. Yet it is manifestly incomplete: it contains no description of gravity, no particle for the dark matter that outweighs ordinary matter fivefold, no explanation for why the universe is made of matter rather than antimatter, and in its original form no neutrino mass. It is a spectacularly accurate effective description, not the final word.
When the Large Hadron Collider smashes protons and the debris is tallied, essentially every event, jets of hadrons, muon tracks, missing energy carried off by neutrinos, is predicted, to within measured uncertainties, by Standard Model calculations.
The Standard Model reproduces collider data across many orders of magnitude in probability, its greatest and most frustrating triumph.
The Standard Model is renormalizable, meaning its infinities can be systematically absorbed into a finite set of measured parameters; this technical property is what makes its ultra-precise predictions possible in the first place.