Covert networks refer to criminal organizations that operate outside the boundaries of the law; they can be mainly classified as terrorist networks and criminal networks. We consider how Social Network Analysis (SNA) is used to analyze such networks in order to attain a greater knowledge of criminal behavior. In fact, SNA allows examining the network structure and functioning by computing relevant metrics and parameters to identify roles, positions, features, and other network functioning that are not otherwise easily discovered at first glance. This is why Law Enforcement Agencies (LEAs) are showing growing interest in SNA, which is also used to identify weak spots and disrupt criminal groups. This paper provides a literature review and a classification of methods and real-case applications of disruption techniques. It considers covert network adaptability to such dismantling attempts, herein referred to as resilience. Critical problems of SNA in criminal studies are discussed, including data collection techniques and the inevitable incompleteness and biases of real-world datasets, with the aim of promoting a new research stream for both dismantling techniques and data collection issues.