In around 1970, Louis Nirenberg proposed the problem of "Prescribing Gaussian curvature on the sphere". The question has led to one of the most active and exciting research field in geometric analysis. In this talk, we will discuss an extension of this question to "Q-curvature", which on manifolds of dimension four, is a natural analogue of the Gaussian curvature on compact surfaces. We will cover some of the analytic and geometric aspects and some most recent development in this research field.