The localized surface plasmons in metal nanostructures under optical excitation will lead to near-field localization and enhancement, which have shown important applications in surface enhancement spectroscopy, ultra-sensitive sensing, microfluidic chip, enhanced optical force, etc. The plasmon resonance and the resulting electric field enhancement strongly depend on wavelength and structure geometry. As a result, the optical force will be closely related to the field distribution, that is, the optical force can be used to manipulate and sort plasmonic metal structures. The large near-field enhancement and gradient of metal nanoparticle aggregates can also be used as a " plasmonic tweezer” to manipulate other particles. Furthermore, in the case of changing the incident polarization and even for a new type of structured laser beam, the optical manipulation has a higher degree of freedom. In this review, having briefly introduced the plasmon-enhanced optical force, we focus on the recent advances in the following three aspects: 1) the manipulation of plasmonic nanoparticles by optical tweezer, 2) the manipulation of other particles by plasmonic tweezer, and 3) dependence of plasmonic optical force on the polarization, optical angular momentum, structured light and the structured chirality. Comparing with other topics of plasmon- enhanced light-interactions, there is plenty of room for further developing the plasmon-enhanced optical force and optical manipulation. Several research trends can be foreseen. 1) More precise optical manipulating and sorting of nanoparticles (even sub-nanometer). For example, more sensitive special resonant modes (e.g. Fano resonance) of plasmonic nanostructure can be utilized. For some nanostructures with small feature sizes, especially when the gap size is close to 1 nm, the non-local effect has a certain effect on the plasmon resonance. Therefore, when calculating the optical force in this case, non-local effects and possibly other quantum effects should be considered. 2) Richer laser fields, that is, using various new structured fields and chiral structures provides a higher degree of freedom for the optical forces and optical manipulation. Also, the localized surface plasmons can be combined with propagating surface plasmons. 3) Wider applications of plasmonic optical forces, especially in combination with other effects and even interdiscipline, e.g. enhanced spectroscopy, enhanced single particle chemical reactions, nonlinear optical effects, and photothermal manipulations.