Predicting heterogeneous cell responses to chemical or genetic perturbations at the level of single cells is crucial for deciphering molecular processes and obtaining a better understanding of function and disease. While the advent of single-cell high-throughput methods may make this task look easy, their destructive nature prevents us from observing the same cell before and after a perturbation. To predict a patient's response to different treatments, one needs to thus re-align unpaired snapshots of cell populations pre- and post-treatment and predict for each cell its corresponding perturbed state after treatment. In addition, while massively parallel high-resolution methods such as Perturb-Seq allow phenotyping in an unprecedented resolution, their scale and randomized nature pose additional challenges and requirements to machine learning algorithms for modeling perturbation responses. In this talk, I demonstrate how we can use neural optimal transport (OT) methods to solve these puzzles and predict treatment responses optimally on the single-cell level. These novel deep learning approaches inspired by OT theory not only achieve a new state-of-the-art with substantial quantitative improvements to prior works but also open new frontiers in a current large-scale clinical study to predict treatment responses of unseen patients. Beyond that, neural optimal transport schemes can be extended to various experimental and biological settings, and for example, adapt to the randomized and composite nature of large-scale profiling technologies, predict responses to combination therapies, or model high levels of apoptosis and proliferation emerging in cellular perturbation responses.