  A geometrical form of the supersymmetry conditions for D-branes on arbitrary
type II supersymmetric backgrounds is derived, as well as the associated BPS
bounds. The treatment is general and allows to consider, for instance,
non-static configurations or D-branes supporting a non-vanishing electric flux,
hence completing previous partial results. In particular, our discussion
clarifies how the notion of calibration can be extended in order to be
applicable to the most general supersymmetric configurations. As an
exemplifying preliminary step, the procedure followed is first applied to
fundamental strings.
