The focus of this thesis was the investigation of the complex dynamics of solid-fluid systems. These systems are of great industrial importance, such as in methane clathrate formation in sub-sea pipelines. As well as being crucial to furthering our understanding of various natural phenomena, such as the rate of rain droplet formation in clouds. We began by considering the problem of the orbits tracked by ellipsoids immersed in viscous and inviscid environments. This investigation was carried out by a combination of analytical and numerical techniques: direct numerical simulations of resolved full-coupled solid-fluid systems, analysis the Kirchhoff-Clebsch equations for the case of inviscid flows, and characterising dynamics through advanced techniques such as recurrence quantification analysis. We demonstrate that the ellipsoid tracks a chaotic orbit not only in an inviscid environment but also when submerged in a viscous fluid, under specific conditions. Under inviscid environments, an ellipsoid subject to arbitrary initial conditions of linear and angular momentum demonstrates chaotic orbits when all the three axes of the ellipsoid are unequal, in agreement with the Kozlov and Onishchenko’s theorem of non-integrability of Kirchhoff’s equations and also with Aref and Jones’s potential flow solution. We then extended our methodology to understand the dynamics of a single ellipsoid tumbling in a viscous environment with the presence of both passive and viscosity coupled tracers in addition to the chaotic dynamics predicted by the Kirchhoff-Clebsch equations. Our results show that the bodies move along from viscosity gradients towards minima of the viscous stress. These bodies might become trapped in unstable minima. However, more work is needed to understand the long-term mixing of viscosity coupled tracers. Our direct numerical solver was also extended to include contact models for solid-solid interactions in the simulation domain. The validation of the contact models was presented. Finally, we expand, the theoretical framework of the Kirchhoff-Clebsch equations to account for the presence of multiple bodies. This extension was done by using Hamiltonian mechanics to extend the derivation proposed by Lamb. We present our preliminary result of simulating two solids systems using the extended Kirchhoff-Clebsch equations. The rel- ative orientations of the two solids were found to regularly switch from being correlated to anti-correlated in an otherwise chaotic system. Further work is required to understand the mechanism behind this behaviour.