This mini-review provides an overview of perturbation modelling in single-cell omics, focusing on the recent advancements and technologies used to understand the effects of external influences on cellular physiology. The authors highlight the importance of perturbation modelling in studying disease progression and drug development, emphasizing the role of machine and deep learning tools in transforming complex phenomena into algorithmically tractable tasks. The review covers various single-cell technologies, such as Perturb-seq, CRISPR-seq, and CROP-seq, which enable the study of perturbation responses at the single-cell level. It also discusses different computational methods, including classical statistical models, machine learning architectures, and biologically informed approaches based on gene regulatory networks. The review critically assesses the challenges in single-cell perturbation modelling, such as the lack of standards and benchmarks, and points towards future directions, including the development of perturbation atlases, multi-omics datasets, and causal machine learning for interpretability. The authors conclude by discussing the potential of large foundational models inspired by language models to enhance the field of single-cell perturbation modelling.This mini-review provides an overview of perturbation modelling in single-cell omics, focusing on the recent advancements and technologies used to understand the effects of external influences on cellular physiology. The authors highlight the importance of perturbation modelling in studying disease progression and drug development, emphasizing the role of machine and deep learning tools in transforming complex phenomena into algorithmically tractable tasks. The review covers various single-cell technologies, such as Perturb-seq, CRISPR-seq, and CROP-seq, which enable the study of perturbation responses at the single-cell level. It also discusses different computational methods, including classical statistical models, machine learning architectures, and biologically informed approaches based on gene regulatory networks. The review critically assesses the challenges in single-cell perturbation modelling, such as the lack of standards and benchmarks, and points towards future directions, including the development of perturbation atlases, multi-omics datasets, and causal machine learning for interpretability. The authors conclude by discussing the potential of large foundational models inspired by language models to enhance the field of single-cell perturbation modelling.