Cell differentiation is an important process in living organisms. Differentiation is mostly based on binary decisions with the progenitor cells choosing between two specific lineages. The differentiation dynamics have both deterministic and stochastic components. Several theoretical studies suggest that cell differentiation is a bifurcation phenomenon, well-known in dynamical systems theory. The bifurcation point has the character of a critical point with the system dynamics exhibiting specific features in its vicinity. These include the critical slowing down, rising variance and lag-1 autocorrelation function, strong correlations between the fluctuations of key variables and non-Gaussianity in the distribution of fluctuations. Recent experimental studies provide considerable support to the idea of criticality in cell differentiation and in other biological processes like the development of the fruit fly embryo. In this Review, an elementary introduction is given to the concept of criticality in cell differentiation. The correspondence between the signatures of criticality and experimental observations on blood cell differentiation in mice is further highlighted.