Two dwarf galaxies begin their lives in dark matter haloes of identical mass. They start their evolution with identical baryonic properties - but then one twin falls into a galaxy cluster, while the other one stays out in the field. The cluster environment alters the baryonic characteristics of the first dwarf: ram pressure removes the gas, harassment increases the random motion of the stars. At some later epoch, the second dwarf also enters the same cluster, and they happen to meet at a crossing point of their orbits. When comparing them, the observers notice that the first dwarf looks much older than the second one, concluding that the strong gravitational force inside the cluster was responsible for that. - But wait: is it even true that a dwarf in an overdense region begins with the same initial properties than a dwarf in an underdense region? Aren't there more evolutionary effects than just the influence of the galaxy cluster? In this talk, I will touch on several aspects of our understanding - as well as some misunderstandings - of dwarf galaxy evolution under environmental influence. Paradoxically, it seems that at least a fraction of the old dwarfs arrived only recently to the cluster environment.