Be it to aerate a glass of wine before tasting, to accelerate a chemical reaction, or to cultivate cells in suspension, the "swirling" (or orbital shaking) of a container ensures good mixing and gas exchange in an efficient and simple way. Despite being used in a large range of applications this intuitive motion is far from being understood and presents a richness of patterns and behaviors which has not yet been reported. The present research charts the evolution of the waves with the operating parameters identifying a large variety of patterns, ranging from single and multiple crested waves to breaking waves. Free surface and velocity fields measurements are compared to a potential sloshing model, highlighting the existence of various flow regimes. Our research assesses the importance of the modal response of the shaken liquids, laying the foundations for a rigorous mixing optimization of the orbital agitation in its applications. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874612].