The present status of elastic pp and pp̄ scattering in the high-energy domain is reviewed, with emphasis on the forward and near-forward regions. The experimental techniques for measuring σtot, ρ, 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 pp and pp̄, obtained from experimental data for σtot and ρ. It is found that a good fit can be obtained using only five parameters (with a cross section rising as ln2s), over the energy range 5<s<62 GeV. The possibilities that (a) the cross section rises only as lns, (b) the cross section rises only locally as ln2s, and eventually goes to a constant value, and (c) the cross-section difference between pp and pp̄ does not vanish as s-->∞ 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 pp̄ and the pp systems. Predictions of all of the elastic scattering parameters are made at ultrahigh energies, and are compared to the available SPS collider measurements.