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In the active distribution networks (ADNs), the emerging trend of high penetration of sustainable energy sources such as wind turbines, photovoltaics, and the forthcoming integration of energy storage devices and additional dynamic loads like plug‐in‐electric vehicles (PEVs) influences to change the nature of electric distribution networks. Consequently, it deteriorates power quality and reliability in terms of unacceptable voltage rise‐drop, harmonic distortion, voltage unbalance, and excessive power loss. In this context of transition into the active distribution network, the probabilistic optimal power flow (P‐OPF) in the ADN is considered an important tool that helps the distribution grid operators for defining the optimal settings of the system's control variables. However, the optimal solution of P‐OPF becomes highly complex while considering the multiple variables, time‐varying characteristics and operational uncertainties associated with sustainable resources, consumer behaviour and electricity market prices. This review aims at promoting the research and discussion of P‐OPF studies in the context of ADNs characteristics and challenges. First, we perform a data‐driven and visualized scientometric analysis of 1988 quality documents retrieved from the Scopus during the last ten years using VOSviewer software. Second, an in‐depth investigation of the recent and emerging techniques for solving the P‐OPF problem is presented. Third, a set of recommendations and highlights of future challenges for P‐OPF in ADNs are offered. The review findings showed high interest among the scientific community in sustainable energy source integration, given the recent rise in publications and citations. Also, there is still a lack of innovative optimization techniques that can adequately handle the current issues associated with P‐OPF and objectives with fair computational efficiency and accuracy. Finally, this paper offers a guide for P‐OPF researchers to navigate the recent studies considering the sustainable sources, spot the new research frontiers, and identify the most impactful countries and publishers. [ABSTRACT FROM AUTHOR]