How can we help an investigator to efficiently connect the dots and uncover the network of individuals involved in a criminal activity based on the evidence of their connections, such as visiting the same address, or transacting with the same bank account? We formulate this problem as Active Search of Connections, which finds target entities that share evidence of different types with a given lead, where their relevance to the case is queried interactively from the investigator. We present RedThread, an efficient solution for inferring related and relevant nodes while incorporating the user's feedback to guide the inference. Our experiments focus on case building for combating human trafficking, where the investigator follows leads to expose organized activities, i.e. different escort advertisements that are connected and possibly orchestrated. RedThread is a local algorithm and enables online case building when mining millions of ads posted in one of the largest classified advertising websites. The results of RedThread are interpretable, as they explain how the results are connected to the initial lead. We experimentally show that RedThread learns the importance of the different types and different pieces of evidence, while the former could be transferred between cases.