Shrimps are islands of periodicity within a chaotic sea in phase and parameter spaces of dimensions larger than one. Islands of different periodicities have recently been shown to be connected by spirals that emanate from a joint focal point, paving ways to wander around in parameter space without ever crossing the chaotic sea. We discuss the shrimp building and scaling principles as well as the influence of individual system properties. While the emergence of shrimps has abundantly been demonstrated for artificial systems, we discuss here in detail evidence of rich hierarchies of shrimps in experimental systems. We finally pinpoint the importance of shrimps in the field of bioinformatics.