Many multi-agent systems in nature comprise agents that interact with, and respond to, the dynamics of their environment. For example, fish school based on the fundamental fluid phenomena of vortex shedding, birds shed leading-edge vortices in formation for flocking, and E. coli bacteria secrete and push against a surrounding medium to meander in swarms. In this thesis, we investigate the dynamics and control of three mechanical systems in which agents interact with a surrounding medium to affect motion. We simplify agent-medium interactions by first considering a passively compliant agent that sits atop a platform capable of translational motion, introduce reduced equations for the system using notions of symmetry and nonholonomic momentum, and provide proof for a particular stable behavior under arbitrary deformations of the elastic element modeling its compliance. We then direct our focus to the frequency response and control of passive agents by assuming actuation of the platform, discuss rich dynamical features arising from periodic actuation, and develop rules by which control can be exerted  to collect and disperse multiple such agents. We then leverage our understanding of this single agent model to inform a geometric treatment of two agents atop a platform, again invoking symmetry and nonholonomic reduction for analysis. We motivate the use of the reduced dynamics for this system in constructing proofs for stability and an entrainment phenomenon observed in simulation. Finally, we introduce the dynamic model for a novel fluid-propulsive aquatic agent in an ideal fluid that exerts control over its motion using impulsive fluid-ejection events to move in its environment. We present an analysis concerning the entrainment of a cylindrical-shaped aquatic agent in flows induced by neighboring agents, present preliminary results of a position-stabilizing controller using impulsive fluid-ejection events, and discuss the next steps necessary to model multiple such agents in an inviscid fluid.