For a real number α and a natural number N, the Sudler product at stage N is defined as P_N(α) = ∏_1≤r≤N 2 |sin πrα| . In my talk, I will focus on the asymptotics of P_N(α) as N → ∞. It is known that liminf P_N(α) = 0 for almost all α, including all well approximable α. However, like in many cases in the Diophantine approximation, the most interesting situation is when α is badly approximable, i.e., all partial quotients of its continued fraction expansion are uniformly bounded from above. The result in this direction was obtained by Verschueren and independently by Grepstad, Kaltenböck, and Neumüller. They showed that for α = [0; 1, 1, 1, . . .] = (√5+1)/2 one has liminf P_N(α) > 0. I will survey results in this area and explain how the behaviour of P_N(α) depends on the Diophantine properties of α. I will also speak about my recent joint result with Manuel Hauke devoted to the set of α such that liminf P_N(α) > 0.