This chapter examines four three-dimensional vortex flow phenomena. The first phenomenon is reconnection of a pair of equal anti-parallel vortices and of initially orthogonal vortex tubes. The second phenomenon involves interaction of vortices of different sizes and strengths. We discuss a series of four processes—vortex entrainment, wrapping, polarization, and stripping. Specific examples include entrainment of a vortex ring into a columnar vortex and reconnection of unequal anti-parallel vortices. Multiscale vortex interactions resulting from vortex interaction with a sphere, a circular cylinder, and a blade are also discussed. The third phenomenon is vortex breakdown, for which we review different breakdown types, examine the Brown-Lopez necessary condition for breakdown, and review Benjamin’s dual-states model. Plug flow model predictions are developed and compared to data. The fourth phenomenon involves cutting of a columnar vortex by a thin blade, in which vortex lines within the columnar vortex reconnect to those within the blade boundary layer. Details of the vortex cutting process are examined, and a simplified solution for response to cutting of a vortex with axial flow is compared to experimental and numerical simulation results.