1. to express possession
Das ist das Haus meines Vaters.
In modern German the genitive is mainly used in written formal language. In spoken informal language phrases with the preposition von are used rather than the genitive. (das Zimmer von meinem Bruder instead of das Zimmer meines Bruders).
2. always after the following prepositions: während, wegen, statt, trotz, ….
Wegen des Regens kommen wir nicht.