Two stars side - pattern 1
The popular move next for Black is . In answer White usually takes steps to limit Black's framework, for example at the marked points. Even though isn't a rapidly developing play, it is quite urgent for White to pay attention to this area.
The choice of has been seen in recent years: it indicates that the original third line play was made in connection with the lower left corner, and that the left side is still important. The circle-marked point is now one vital point for both sides. White may also choose the square-marked point.
In these examples Black avoids trying for a double-wing formation based on 4-4:
Assuming White to play, this is the widest path sequence: effectively this is a joseki. That does assume that is a strong stone.
This choice of is only appropriate when can become weak. That is, exactly when the exchange Black a- White b will cause Black trouble. Otherwise White would get a heavy group here, without much compensation.
See Two stars side - pattern 2 for the case in which is on the fourth line.