Life is a history-driven process, pervaded by memories at many scale, from the molecular assembly patterns inside a cell up to the cultural organization of human societies. Memory can be defined as a trace of a past event that serves as an effective tool for reacting to, or anticipate, a future recurrence of a similar event. For a long time, the idea that the predictability of environmental trajectories can be used by an organism to adapt was restricted to understanding complex behavior in animals, following the seminal work of Ivan pavlov and collaborators in the beginning of the 20th century. Recent investigations have however started to address a possible generalization of this phenomenon by studying anticipatory behaviors in microorganisms in time-structured environments. We have recently set-up an original experimental approach to study microbial evolution in the context of variable environments, for which predictive behavior is possible on the basis of the time-structure of the environment. We believe that this paradigm shift in understanding microbial behavior raises many fundamental questions, in particular concerning its evolutionary implications.