The present status of elastic $\mathrm{pp}$ and $p\overline{p}$ scattering in the high-energy domain is reviewed, with emphasis on the forward and near-forward regions. The experimental techniques for measuring ${\sigma }_{\mathrm{tot}}$, $\rho$, and $B$ are discussed, emphasizing the importance of the region in which the nuclear and Coulomb scattering interfere. The impact-parameter representation is exploited to give simple didactic demonstrations of important rigorous theorems based on analyticity, and to illuminate the significance of the slope parameter $B$ and the curvature parameter $C$. Models of elastic scattering are discussed, and a criterion for the onset of "asymptopia" is given. A critique of dispersion relations is presented. Simple analytic functions are used to fit simultaneously the real and imaginary parts of forward scattering amplitudes for both $\mathrm{pp}$ and $p\overline{p}$, obtained from experimental data for ${\sigma }_{\mathrm{tot}}$ and $\rho$. It is found that a good fit can be obtained using only five parameters (with a cross section rising as ${\ln }^{2}s$), over the energy range $5<\mathrm{}\sqrt{s}<62\mathrm{}$ GeV. The possibilities that (a) the cross section rises only as $\ln s$, (b) the cross section rises only locally as ${\ln }^{2}s$, and eventually goes to a constant value, and (c) the cross-section difference between $\mathrm{pp}$ and $p\overline{p}$ does not vanish as $s\to \infty$ are examined critically. The nuclear slope parameters $B$ are also fitted in a model-independent fashion. Examination of the fits reveals a new regularity of the $p\overline{p}$ and the $\mathrm{pp}$ systems. Predictions of all of the elastic scattering parameters are made at ultrahigh energies, and are compared to the available SPS collider measurements.

DOI:https://doi.org/10.1103/RevModPhys.57.563