There is a recognized and growing need for rapid and efficient cell assays, where the size of microfluidic devices lend themselves to the manipulation of cellular populations down to the single cell level. An exceptional way to analyze cells independently is to encapsulate them within aqueous droplets surrounded by an immiscible fluid, so that reagents and reaction products are contained within a controlled microenvironment. Most cell encapsulation work has focused on the development and use of passive methods, where droplets are produced continuously at high rates by pumping fluids from external pressure-driven reservoirs through defined microfluidic geometries. With limited exceptions, the number of cells encapsulated per droplet in these systems is dictated by Poisson statistics, reducing the proportion of droplets that contain the desired number of cells and thus the effective rate at which single cells can be encapsulated. Nevertheless, a number of recently developed actively-controlled droplet production methods present an alternative route to the production of droplets at similar rates and with the potential to improve the efficiency of single-cell encapsulation. In this critical review, we examine both passive and active methods for droplet production and explore how these can be used to deterministically and nondeterministically encapsulate cells.