Bedside caregivers assess infants' pain at constant intervals by observing specific behavioral and physiological signs of pain. This standard has two main limitations. The first limitation is the intermittent assessment of pain, which might lead to missing pain when the infants are left unattended. Second, it is inconsistent since it depends on the observer's subjective judgment and differs between observers. Intermittent and inconsistent assessment can induce poor treatment and, therefore, cause serious long-term consequences. To mitigate these limitations, the current standard can be augmented by an automated system that monitors infants continuously and provides quantitative and consistent assessment of pain. Several automated methods have been introduced to assess infants' pain automatically based on analysis of behavioral or physiological pain indicators. This paper comprehensively reviews the automated approaches (i.e., approaches to feature extraction) for analyzing infants' pain and the current efforts in automatic pain recognition. In addition, it reviews the databases available to the research community and discusses the current limitations of the automated pain assessment.