Significance Momentum is an important backbone of wave fields such as electromagnetic waves, matter waves, sound waves, and fluid waves. As the carriers of electromagnetic waves, photons possess both linear and angular momenta, which can interact with matter and generate optical forces. The technique, or optical tweezers which utilize optical forces to manipulate micro/ nano-objects, was established by Arthur Ashkin between the 1970s and 1980s. Optical tweezers have unparalleled advantages in capturing and manipulating microscopic particles and provide new research tools for research fields such as biomedicine, physics, and chemistry. In 1997, Steven Chu, Claude Cohen- Tannoudji, and William D. Phillips won the Nobel Prize in Physics for employing optical forces to achieve atomic cooling. It was later in 2018 that Ashkin won half of the Nobel Prize in Physics for his pioneering contributions to optical tweezers and implementing them for biomedical applications. Optical forces adopted in optical manipulation mainly include two popular types of radiation pressure and optical gradient force. The radiation pressure is the force along the direction of the Poynting vector due to the light scattering and absorption and has important applications in atomic cooling, optical sorting, and particle propulsion. The optical gradient force is the force generated by the inhomogeneous intensity or phase distribution of the light field, with great potential in numerous physical and biomedical applications. The optical lateral force (OLF) is an extraordinary force that is perpendicular to the light propagation direction and independent of the intensity or phase gradient of the light field. It is related to the intrinsic and structural properties of light and matter. The strategy to realize an OLF is to break the system symmetry to make photons exert transverse momenta and consequently generate optical forces on particles. Since OLF was first proposed by Nori s and Chan s groups on the same day in 2014, various methods and mechanisms have been reported to configure and explore OLF, such as utilizing the spin and orbital momenta of light, coupling of light and particle chirality, spin- orbit interaction (SOI), and surface plasmon polariton (SPP). In the past ten years, the understanding of transverse momenta and relevant light-matter interaction has reached a new stage. Transverse momentum, whether linear or angular, is closely related to OLF since the optical force is a consequence of momentum exchange or translation between light and matter. For example, transverse spin momentum, also known as the Belinfante spin momentum ( BSM), or transverse spin angular momentum ( SAM), can generate spin-correlated OLF. Additionally, the imaginary Poynting momentum (IPM) can also induce OLF. The chirality of particles can couple with light and generate transverse energy flux and force near the surface. The conversion of spin angular momentum to orbital angular momentum, or the so- called SOI, endows a new way to generate the OLF. Investigations of such extraordinary transverse light momenta and OLF deepen the understanding of light- matter interactions and have tremendous applications in bidirectional enantioselective separation, meta-robots, spintronics, and quantum physics. Progress We review the current theoretical and experimental research progress on OLF, including different mechanisms, experimental methods, and potential applications. We first introduce some fundamentals of transverse momenta, and representative mechanisms for generating OLF from both theoretical and experimental perspectives, including the BSM, chirality, SOI, IPM, and some other effects such as heat, electricity, bubbles, and topology. Meanwhile, we review some representative applications based on OLF, such as meta- robots, particle sorting, and some other biomedical and chemical applications. Finally, we summarize this research direction and provide our vision of new physical mechanisms and more applications that may emerge in the future. Conclusions and Prospects Momentum and force are two fundamental quantities in electromagnetics. With the innovation and burgeoning development of optical theories of transverse light momenta, mechanisms of OLF are also advancing. The optical force has also become an essential platform and effective tool for testing and validating numerous optical phenomena including transverse momenta. Traditional optical gradient force and radiation pressure have been widely studied in the past four decades, and their technical limitations in some applications have been well comprehended. Some peculiar optical forces discovered in recent years such as the optical pulling force and OLF are playing increasingly important roles in high-precision optical manipulation. OLF provide new possibilities for nanometer-precision sorting, enantioselective separation, and minuscule momentum probing. Additionally, unprecedented advantages of metasurfaces in electromagnetic wave guidance and steering also present more possibilities for manipulating particles. Especially in recent years, with the rapid development of nanofabrication technology, a type of meta-robot driven by the OLF has emerged. Although it has not been implemented in practice, its interesting properties and the new degree of freedom in optical manipulation are expected to find many biomedical applications in the future, such as cargo transporting, biotherapy, and local probing. We can also envision various biological applications of OLF, such as bilaterally sorting and binding tiny bioparticles, cargo transporting using metavehicles, stretching and folding DNA and protein molecules in line-shaped beams, enantioselective separation, and high- sensitive sensing by the helical dichroism. Therefore, we can conclude that with the development of modern optics and photonics, the two interrelated quantities of momentum and force will be explored more deeply and have wide applications in material science, biophysics, quantum science, spintronics, optical manipulation, and sensing.
