I will present aspects of a theory of space-time integral currents with bounded variation in time. This is motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations (this model is joint work with T. Hudson). The classical scalar BV-theory can be recovered as the 0-dimensional limit case of this BV space-time theory. However, the emphasis is on evolutions of higher-dimensional objects, most notably 1D loops moving within 3D domains (i.e., the codimension 2 case), which corresponds to dislocation dynamics in a material specimen. Based on this, I will discuss the notion of Lipschitz deformation distance between integral currents, which arises physically as a (simplified) measure of dissipation. In particular, I will explain its relation to the boundaryless Whitney flat metric.