In this talk I will give a brief introduction to probability measures on compact quantum groups. As examples, two types of such probability measures will be discussed, the idempotent ones and the infinitely divisible ones. More precisely, we will (1) decide all the idempotent probability measures on Sekine quantum groups A_k, k ? 2, and give their lattice structure for k prime, which answers a question of Franz and Skalski in 2009; (2) characterise all the infinitely divisible probability measures on finite quantum groups, which recovers two results (Bge's 1959 and Parthasarathy's in 1972) from different directions.

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