I will discuss the question of sampling from the p-spin Gibbs measure. Whether or not this task is efficiently possible is connected to the geometric properties of the measure, which undergoes a sequence of phase transition phenomena as the temperature is changed. I will present the phase digram and discuss what is supposed to happen in each phase. I will then construct an efficient sampling algorithm in a large sub-interval of temperatures where this task is believed to be possible, and rule out a large sub-family of efficient algorithms when it is not. The latter obstruction is obtained by proving strong notions of shattering and chaos for the measure.