A child born to Austrian parents is an Austrian citizen. If the parents are married at the time of birth, Austrian citizenship of either the mother or the father is sufficient, so long as the child was born after January 9th, 1983. For children born prior to that date, the father must have been an Austrian citizen - children born to an Austrian mother married to a non-Austrian father do not qualify. If the parents are not married, however, a father cannot pass on Austrian citizenship, whereas a mother can.
Should the parents happen to marry at some time after the birth, citizenship is automatically granted to the child retroactively. If the child is over 14 at that time, however, his or her consent is needed.