Swirling motion is an essential phenomenon that significantly influences numerous biological processes, such as the mixing of molecular components within living cells, nutrient transport, the structural changes of the cytoskeletons of contractile cells and the rearrangement of multicellular systems caused by collective cell migration. The dynamical relationship between subcellular and supracellular rearrangements enhances cell migration and contributes to tissue homeostasis. However, the basic mechanisms that drive swirling motion in biological contexts remain a matter of ongoing inquiry. Several complex biological systems, including synovial fluid, blood, mucus, cytoskeleton, and epithelial and mesenchymal multicellular systems, are examined in the context of possible swirling motion. Despite their diverse structures and fluid properties, they all exhibited swirling behaviour. Shared characteristics among these systems include: (i) a heterogeneous distribution of density and mechanical stress, (ii) viscoelastic properties, (iii) anisotropic behaviour, and (iv) non-uniform flow patterns. This multifaceted phenomenon is analysed through the integration of experimental findings from the existing literature with modelling considerations, aiming to identify the primary physical factors that contribute to the occurrence of swirling motion such as: lift force and normal stress differences that appear as a consequence of generated shear stress.