Particles and fields interact in combinations that appear to be well-modelled by the thoery of mathematical groups. The exploration of this relationship is called Gauge Theory.
We delineate the interactions below; supporting evidence is emphasized subsequently.
Quantum Electrodynamics is the theory of electric charge and its interactions, electromagnetism. (In common experience, we perceive electricity and magnetism as two separate phenomena. Special relativity shows that one is an unavoidable adjunct of the other: in a frame co-moving with charge, it never generates a magnetic field.) Mathematically, QED is the simplest possible ('rank' 1) interaction theory for quantum particles.
All of chemistry and much of engineering.
The weak interaction mediates the transformation of matter from one charge state to another. The mathematical theory of weak interactions is exactly one rank above that of QED.
Radioactive decay, high-energy lepton physics (including creation of quark-antiquark pairs in electron-positron collisions).
Quantum chromodynamics describes the interactions that bind quarks (partial-charge states) into nucleons (protons and neutrons). The progression continues: the mathematical theory is exactly one rank more complex than that of the weak interactions.
Baryon spectroscopy, kinematics of high-energy colliding proton beams.
Gravitation, in its three-dimensional manifestation, is in some measures, only one rank more complex than quantum chromodynamics.
Each field is generated by a particle charge. Respectively for each interaction, these are electric charge, isospin, color and mass.