To develop parallel imaging techniques that simultaneously exploit coil sensitivity encoding, image phase prior information, similarities across multiple images, and complementary k-space sampling for highly accelerated data acquisition. We introduce joint virtual coil (JVC)-generalized autocalibrating partially parallel acquisitions (GRAPPA) to jointly reconstruct data acquired with different contrast preparations, and show its application in 2D, 3D, and simultaneous multi-slice (SMS) acquisitions. We extend the joint parallel imaging concept to exploit limited support and smooth phase constraints through Joint (J-) LORAKS formulation. J-LORAKS allows joint parallel imaging from limited autocalibration signal region, as well as permitting partial Fourier sampling and calibrationless reconstruction. We demonstrate highly accelerated 2D balanced steady-state free precession with phase cycling, SMS multi-echo spin echo, 3D multi-echo magnetization-prepared rapid gradient echo, and multi-echo gradient recalled echo acquisitions in vivo. Compared to conventional GRAPPA, proposed joint acquisition/reconstruction techniques provide more than 2-fold reduction in reconstruction error. JVC-GRAPPA takes advantage of additional spatial encoding from phase information and image similarity, and employs different sampling patterns across acquisitions. J-LORAKS achieves a more parsimonious low-rank representation of local k-space by considering multiple images as additional coils. Both approaches provide dramatic improvement in artifact and noise mitigation over conventional single-contrast parallel imaging reconstruction. Magn Reson Med 80:619-632, 2018. © 2018 International Society for Magnetic Resonance in Medicine. © 2018 International Society for Magnetic Resonance in Medicine.