In this paper, the author demonstrates that the leading logarithms in high-energy scattering can be obtained by evolving nonlocal operators—straight-line ordered gauge factors—with respect to the slope of the straight line. These operators, known as Wilson-line gauge factors, correspond to fast-moving quarks along straight lines. The small-x behavior of structure functions is governed by the evolution of these operators with respect to deviations from the light cone, which serve as a "renormalization point." The BFKL equation is shown to be a nonlinear evolution equation for these Wilson-line operators, containing more information than the usual BFKL equation, such as the triple vertex of hard pomerons in QCD. The paper discusses the high-energy behavior of QCD amplitudes, particularly the structure function $ F_2(x, Q^2) $, which increases rapidly at small x. The BFKL equation, which governs this behavior, has issues with unitarity and is not fully rigorous. The author proposes a gauge-invariant operator expansion for high-energy amplitudes, using Wilson-line operators ordered along light-like lines. These operators are essential for separating small- and large-distance contributions to high-energy amplitudes. The paper also discusses the Regge limit, where the high-energy behavior of scattering amplitudes is studied. The quark propagator in an external gluon field is analyzed, and the impact factor is derived, which is crucial for calculating scattering amplitudes. The impact factor is shown to be independent of the energy scale $ s $, and it is used to express the scattering amplitude in terms of Wilson-line operators. The paper concludes with a discussion on regularized Wilson-line operators, which are necessary to handle the longitudinal divergence in the matrix elements of these operators. These operators are analogous to local renormalized operators for high-energy amplitudes and are essential for a proper gauge-invariant description of high-energy scattering. The paper emphasizes the importance of these operators in separating small- and large-distance contributions to high-energy amplitudes and in providing a gauge-invariant generalization of the BFKL equation.In this paper, the author demonstrates that the leading logarithms in high-energy scattering can be obtained by evolving nonlocal operators—straight-line ordered gauge factors—with respect to the slope of the straight line. These operators, known as Wilson-line gauge factors, correspond to fast-moving quarks along straight lines. The small-x behavior of structure functions is governed by the evolution of these operators with respect to deviations from the light cone, which serve as a "renormalization point." The BFKL equation is shown to be a nonlinear evolution equation for these Wilson-line operators, containing more information than the usual BFKL equation, such as the triple vertex of hard pomerons in QCD. The paper discusses the high-energy behavior of QCD amplitudes, particularly the structure function $ F_2(x, Q^2) $, which increases rapidly at small x. The BFKL equation, which governs this behavior, has issues with unitarity and is not fully rigorous. The author proposes a gauge-invariant operator expansion for high-energy amplitudes, using Wilson-line operators ordered along light-like lines. These operators are essential for separating small- and large-distance contributions to high-energy amplitudes. The paper also discusses the Regge limit, where the high-energy behavior of scattering amplitudes is studied. The quark propagator in an external gluon field is analyzed, and the impact factor is derived, which is crucial for calculating scattering amplitudes. The impact factor is shown to be independent of the energy scale $ s $, and it is used to express the scattering amplitude in terms of Wilson-line operators. The paper concludes with a discussion on regularized Wilson-line operators, which are necessary to handle the longitudinal divergence in the matrix elements of these operators. These operators are analogous to local renormalized operators for high-energy amplitudes and are essential for a proper gauge-invariant description of high-energy scattering. The paper emphasizes the importance of these operators in separating small- and large-distance contributions to high-energy amplitudes and in providing a gauge-invariant generalization of the BFKL equation.