It is known that almost all cubic graphs are hamiltonian (see here)
However, I did not find any information about non-hamiltonian cubic graphs online. If you know some properties/literature about non-hamiltonian cubic graphs I would appreciate if you let me know. More specifically, the question that interests me is how the cubic graphs that are not Hamiltonian are different from Hamiltonian cubic graphs (what properties do they have that makes them not Hamiltonian)?