By Descent (Before 2007)
If child born overseas to Australian parent: automatic Australian citizenship (grandfather clause). If born after Jan 1, 2007: registration required.
Born After 2007
Child born overseas to Australian parent: eligible for citizenship by descent (not automatic). Parent must apply (Form 119).
If Parent Becomes Citizen After Birth
Child can acquire citizenship if under 18. Must be legitimate connection (child living in Australia typically).