Harnessing linear and angular momenta of light is one of the cornerstones in modern optics and has found tremendous applications in optical circuits, particle manipulation, metrology, quantum information processing, etc. Emerging theoretical protocols and experimental explorations have created a surge of interest in light lateral momenta and forces, which are perpendicular to the light wave propagation direction. However, there is yet a lack of a comprehensive and holistic overview of transverse momenta (both linear and angular) as well as of optical lateral forces (OLFs). In this article, we first review the most recent transverse momenta including the transverse spin angular momentum, optical skyrmions, as well as lateral momenta from directional side scattering, spin-orbit interaction, and surface plasmon polaritons. Since optical forces result from the momentum exchange between light and matter, the transverse momentum consequently gives rise to intriguing OLFs, which is the second topic of this article. Additional non-trivial lateral forces that combine optics with other effects from thermodynamics, electricity, and microfluidics, are also discussed. It should be emphasized that these momenta and forces ubiquitously exist in a broad range of optical phenomena and have often been neglected due to their unpredicted underlying physics and shortage of experimental means, especially prior to the last decade. © 2023 Optica Publishing Group.