A review is given of problems of the interaction of nucleons. The processes are discussed mainly at energies corresponding to the regions of the minimum and the rise of the total cross sections and to regions covered by the accelerators at Serpukhov and Batavia and the colliding-beam storage rings. Detailed consideration is given to $np$ interactions, including the technique for performing experiments in neutron beams. This is done because accurate experiments in neutron beams have been carried out only recently, and the experimental features of these experiments are not widely known. The article discusses total cross sections, forward elastic scattering, backward elastic scattering ($np$ charge exchange), and diffraction dissociation of nucleons. The equality of the total $np$ and $pp$ cross sections (observed experimentally in the energy range of the Serpukhov accelerator), and the near identity of elastic scattering in the diffraction region, mean from the point of view of the optical model that the distributions of nuclear matter in neutrons and protons in the peripheral regions are practically identical. The equality of the total cross sections is in agreement with the prediction of dual models involving degeneracy of the $\rho$ and $A_2$ trajectories. It is well known that in the $np$ charge-exchange reaction there is also observed a longrange interaction which appears in the form of a very sharp peak at $t\approx0$. The slope of the peak is $\approx1/m^2_\pi$, where $m_\pi$, is the pion mass. The existence of this peak and also the simple kinematic law for variation of the cross section with energy: $E^{-2}$ (observed in experiments up to 30 GeV) are due to the dominant role of pion exchange in the charge-exchange reaction. On going to higher energies (the energy range of the Serpukhov accelerator) changes are observed in the energy behavior of the charge-exchange reaction: $E^{-(1.5-1.6)}$. Changes of this type were predicted in Regge models and are due to the increasing role of $\rho$ and $A_2$ exchanges at high energies. Recently careful studies have been made of the diffraction dissociation of nucleons at high energies (Serpukhov, Batavia, and colliding beams). These studies have revealed a number of features previously unobserved (at energies below 30 GeV), such as the backward peak in the distribution in $\cos\Theta_{GJ}$ in the Gottfried--Jackson coordinate system, the shift of the maximum in the mass spectrum toward higher masses, the approach of the cross section to a constant value at high energies, and other effects. All of the observed effects can be explained with the Deck mechanism if, in addition to one-pion exchange we take into account baryon exchanges and interference.