Experimental single-cell data often presents an incomplete picture due to its destructive nature: 1) we collect certain experimental measurements of cells but lack measurements under different experimental conditions or data modalities; 2) we collect data of cells at certain time points but lack measurements at other time points; or 3) we collect data of cells under certain perturbations but lack data for other types of perturbations. In this article, we will discuss machine learning approaches to address these types of translation and counterfactual problems. We will begin by giving an overview on single-cell biology applications and the relevant translation problems. Subsequently, we will provide an overview of approaches for multidomain alignment and translation in machine learning, including methods based on generative modeling, optimal transport, and causal inference. The bulk of this article will focus on how these approaches have been tailored and applied to important translation problems in single-cell biology, illustrated through concrete examples from our own work. We end with open problems and a perspective on how biology may not only be uniquely suited to being one of the greatest beneficiaries of machine learning but also one of the greatest sources of inspiration for it.