We demonstrate dynamic trapping and computer-controlled manipulation of nanoparticles with plasmonic holograms. Research into plasmonic trapping has been motivated by its potential for enhanced optical forces. However, while holographic optical tweezing has become an indispensible tool to researchers across a wide range of disciplines, the benefits of full computer control over focused trapping sites has not yet been realized for plasmonic tweezing. In this work, by tailoring the illumination pattern of an incident laser beam with a spatial light modulator, the location of a focused plasmonic hotspot can be moved to arbitrary locations across a surface. The trapping hotspot is purely plasmonic, i.e. the incoming laser beam does not directly illuminate the trapped particles and it is constructive and destructive interference of converging plasmon waves that form the mobile trapping sites. Specifically, a computergenerated hologram illuminating around the edges of a silver Bull’s Eye nano-structure generates surface plasmon waves that propagate towards the center. Shifting the phase of the plasmon waves as a function of space around the Bull’s Eye gives complete control over the location of the focus. We show that 200-nm diameter fluorescent nanoparticles trapped in this focus can be moved in arbitrary patterns in the center of the Bull’s Eye structure. This allows, for example, circular motion of the trapped nanoparticle using linearly-polarized light. These results show the versatility of holographically-generated surface plasmon waves for the trapping and manipulation of nanoparticles under full computer control, combining the many benefits of plasmonic tweezing and holographic optical tweezing.