  We report and discuss analytical solutions of the vector nonlinear
Schr\"odinger equation that describe rogue waves in the defocusing regime. This
family of solutions includes bright-dark and dark-dark rogue waves. The link
between modulational instability (MI) and rogue waves is displayed by showing
that only a peculiar kind of MI, namely baseband MI, can sustain rogue wave
formation. The existence of vector rogue waves in the defocusing regime is
expected to be a crucial progress in explaining extreme waves in a variety of
physical scenarios described by multi-component systems, from oceanography to
optics and plasma physics.
