<p>Particle accelerators, originally developed to address fundamental questions about the universe, have become essential to various scientific disciplines. The broad adoption of accelerators was enabled by substantial advancements in beam manipulation techniques, which encompass methods for generating and controlling particle beams to optimize them for specific applications. Most of these manipulations rely on controlling the beam’s correlation in its phase space. While linear control and the correction of low-order nonlinearities have propelled particle accelerators to their current state, the exploration of more advanced control methods may provide new opportunities to achieve unprecedented beam qualities and conditions. Consequently, there is an increasing demand for control over higher-order nonlinearities. A recently developed method utilizing transverse wigglers shows potential in addressing such demands. Active research is also ongoing on diverse applications of the transverse wiggler-based method in various accelerator fields. This paper discusses methods for controlling highly nonlinear correlations and their applications.</p>