Capturing plasticity at realistic dislocation densities with high configurational complexity requires a continuum-leveldiscrete dislocation dynamics (DDD) description. However, many features controlling dislocation motion areinherently atomistic, such as the interaction of dislocations with solutes, precipitates, cracks, interfaces andnucleation. In two dimensions, modeling these phenomena in a multi-scale manner was possible thanks to themethod Coupled Atomistic and Discrete Dislocation dynamics (CADD2d). Here, we present an approach thatextends this multiscale coupling in 3d (CADD3d). The algorithm principle will be described in details, wheredislocations can be described with atomistic resolution intimately coupled to a surrounding continuum domain in full3d. In such a case, individual dislocation lines may span both domains simultaneously, therefore forming hybriddislocations, partially represented with dislocated atoms and partially as discrete lines. Continuum dislocationproperties and atomistic dislocation properties need to match closely. An implementation prototype is presentedbased on the DDD code Paradis and on the MD code LAMMPS, altogether interfaced with the coupling codeLibMultiScale. Simulations of the dynamics of a single hybrid dislocation and of a hybrid dislocation loop willillustrate the potential and robustness of the approach for near-seamless motion of dislocations into, across, andout of the atomistic domain. Finally we present the nucleation of dislocation loops emitted from a Frank-Readsource and then transformed into DD dislocations, demonstrating the possibilities of our framework.