The dynamic behaviour of glassy materials displays strong nonequilibrium effects, such as ageing in simple protocols, memory, rejuvenation and Kovacs effects in more elaborated experiments. We show that this phenomenology may be easily understood in the context of the nonequilibrium critical dynamics of nondisordered systems, the main ingredient being the existence of an infinite equilibrium correlation length. As an example, we analytically investigate the behaviour of the 2D XY model submitted to temperature protocols similar to experiments. This shows that typical glassy effects may be obtained by “surfing on a critical line” without invoking the concept of temperature chaos nor the existence of a hierarchical phase space, as opposed to previous theoretical approaches. The relevance of this phenomenological approach to glassy dynamics is finally discussed.