Although liver transplantation (LT) is performed increasingly for patients with end-stage alcoholic liver disease (ALD), the topic remains controversial. Traditionally, the role of an addiction specialist focused on the screening and identification of patients with a high risk on relapse in heavy alcohol use. These patients were in many cases subsequently excluded from a further LT procedure. Recently, awareness is growing that not only screening of patients but also offering treatment, helping patients regain and maintain abstinence is essential, opening up a broader role for the addiction specialist (team) within the whole of the transplant procedure. Within this context, high-risk assessment is proposed to be an indication of increasing addiction treatment intensity, instead of being an exclusion criterion. In this review we present an overview regarding the state of the art on alcohol relapse assessment and treatment in patients with alcohol use disorders, both with and without ALD. Screening, treatment and monitoring is suggested as central roles for the addiction specialist (team) integrated within transplant centers.