The modern state of the art on forces is based on quantum field theory. Previous "classical" physics theories were eventually undestood as being related to conservation laws, which in turn were associated with global symmetry of space and time. For example, the convervation of angular momentum can be shown to result from the fact that space behaves the same in any direction. Convervation of energy is related to the fact that space behaves the same at any time. Quantum theory has extended this idea to so-called local symmetry. So for example, the imposition of local symmetry on the electron requires that you introduce another field, and that field turns out to be the photon field. It is remarkably elegant.
Electromagnetic and the Weak Nuclear forces have been unified, and the theory predicts experimental results to the limits of measurability. In the case of EM, Richard Feynman's quantum electrodynamic theory has been verified to 10 decimal places.
The Strong Nuclear force has been described by the theory of quantum chromodynamics (quarks, gluons, color, etc), which seems to be qualitatively correct, predictiong the existance and behavior of protons, mesons, etc. However, the nature of the theory has made it difficult to precisely calculate numerical values of known measured quantities like the magnetic moment of the proton. Physicists believe the theory is sound, computers are just not powerful enough to evaluate it yet. The probelm is related to the fact that the nuclear force actually gets stronger at increasing distance, unlike gravity which falls off as 1/distance-squared.
Of course the first theories of gravity were proposed by Newton, and now the most successful theory is Einstein's theory of General Relativity. But Einstein's theory is still "classical", and while it is very accurate, it is not correct. A big unsolved problem in physics today is the development of a quantum field theory of gravity. Gravitation turns out to be quite complex on a quantum level, requiring a tensor field and a spin-2 intermediate boson called a "graviton". Because the force is so weak, it has been difficult to measure these quantum effects. The current theory is based on a plausible extension of the techniques used in QCD and QEW theory, but it is untested because of this problem with the weakness of gravity.
So the holy grail today would be the unifcation of quantum gravitation, quantum chromodynamcis, and quantum electroweak theory. Lots of hard work ahead for physicist. Outdated pre-quantum theories like Heaviside and Heim's are no help. They just aren't in the ballpark today, because those men didn't have access to what is known today about the nature of fundimental physics.