  The large amounts of dust detected in sub-millimeter galaxies and quasars at
high redshift pose a challenge to galaxy formation models and theories of
cosmic dust formation. At z > 6 only stars of relatively high mass (> 3 Msun)
are sufficiently short-lived to be potential stellar sources of dust. This
review is devoted to identifying and quantifying the most important stellar
channels of rapid dust formation. We ascertain the dust production efficiency
of stars in the mass range 3-40 Msun using both observed and theoretical dust
yields of evolved massive stars and supernovae (SNe) and provide analytical
expressions for the dust production efficiencies in various scenarios. We also
address the strong sensitivity of the total dust productivity to the initial
mass function. From simple considerations, we find that, in the early Universe,
high-mass (> 3 Msun) asymptotic giant branch stars can only be dominant dust
producers if SNe generate <~ 3 x 10^-3 Msun of dust whereas SNe prevail if they
are more efficient. We address the challenges in inferring dust masses and
star-formation rates from observations of high-redshift galaxies. We conclude
that significant SN dust production at high redshift is likely required to
reproduce current dust mass estimates, possibly coupled with rapid dust grain
growth in the interstellar medium.
