Electrodermal activity (EDA) measures skin conductivity, reflecting sweat gland activity, and is considered a noninvasive measure of the sympathetic nervous system (SNS). Consequently, EDA has emerged as an informative physiomarker in clinical and nonclinical applications in assessing dynamics of SNS functions. With recent proliferation of the abuse of pain medications, there is a pressing need for objective pain assessment given that a self-pain rating is the only metric doctors use for prescribing medications. To overcome this limitation, there has been increased attention on the use of EDA due to close association between pain and the SNS. With advancements in wearable sensors combined with signal processing and machine learning, it has become more feasible to objectively assess pain using EDA. This paper provides a comprehensive review of recent research related to the use of EDA for objective pain assessment and its clinical applications. Furthermore, this paper discusses the use of recent new developments in signal processing and machine learning techniques, and examines current challenges and future directions that can enable better quantitative assessment of pain using EDA.