Sampling a given target distribution is a ubiquitous problem in physics, which can prove very hard (hard means slow) in some well documented systems where the energy landscape features a host of local minima, at least at low temperatures. Hence the necessity to find ways and means to speed the sampling up to bypass the natural sluggishness of the physical dynamics in these systems. We will consider the worst possible physical system --a glass forming liquid-- and subject it to various acceleration techniques corresponding to distinct time evolutions, the efficiency of which will be critically discussed. We will then use this variety of time evolutions to take a step back and reflect on the nature of the glass transition. We shall conclude by proposing a picture in which seemingly contradicting theories of glasses can be reconciled. In collaboration with F. Ghimenti, L. Berthier, J. Kurchan and G. Szamel.