  Type Ia supernovae have only recently been employed to measure the peculiar
motions of galaxies. The great distances to which SNe Ia can be seen makes them
particularly well-suited to constraining large-scale velocity flows. The high
precision of SN Ia distance measurements limits the contamination of such
measurements by Malmquist or sample selection biases. I review the recent use
of SNe Ia to measure the motion of the Local Group (updated to include 44 SNe
Ia). The direction of the best-fit motion remains consistent with that inferred
from the CMB (though modest bulk flows cannot be ruled out) and inconsistent
with the Lauer-Postman frame. Comparisons between SN Ia peculiar velocities and
gravity maps from IRAS and ORS galaxies yields constraints on the mass density
which gives rise to the gravitationally induced peculiar motions. Indications
are for $\beta$=0.4 from IRAS, and 0.3 from the ORS, with $\beta>0.7$ and
$\beta<0.15$ ruled out at 95% confidence levels from the IRAS comparison. The
contributions of SNe Ia to peculiar velocity studies are limited by statistics,
but the great increase in the recent discovery rate suggests SNe Ia may become
increasingly important in constraining flows.
