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Soft manipulators, renowned for their compliance and adaptability, hold great promise in their ability to engage safely and effectively with intricate environments and delicate objects. Nonetheless, controlling these soft systems presents distinctive hurdles owing to their nonlinear behavior and complicated dynamics. Learning‐based controllers for continuum soft manipulators offer a viable alternative to model‐based approaches that may struggle to account for uncertainties and variability in soft materials, limiting their effectiveness in real‐world scenarios. Learning‐based controllers can be trained through experience, exploiting various forward models that differ in physical assumptions, accuracy, and computational cost. In this article, the key features of popular forward models, including geometrical, pseudo‐rigid, continuum mechanical, or learned, are first summarized. Then, a unique characterization of learning‐based policies, emphasizing the impact of forward models on the control problem and how the state of the art evolves, is offered. This leads to the presented perspectives outlining current challenges and future research trends for machine‐learning applications within soft robotics.