The mobile phone is a relatively new technological tool, versatile and accessible, and very attractive, especially for young people, but whose use involves a risk of abuse and addictive behavior. In recent years there has been increasing interest in this problem, especially in view of the fact that it involves an increasingly younger population. The aim of this paper is to review the current state of scientific knowledge about cell phone addiction/abuse. To this end, a search was carried out in international databases, using the descriptors "mobile phone", "cellular telephones", "addiction" and "abuse", and focusing on prevalence studies, diagnostic tests, associations with psychological variables and gender differences. There is a conceptual vagueness about the concepts of abuse and addiction in relation to mobile phones, and wide disparity in the adoption of diagnostic criteria; moreover, there are numerous instruments for the assessment of these concepts. As a result, the estimated prevalence ranges from 0-38%, depending on the scale used and the characteristics of the population studied. Surprisingly, self-attribution of cell phone addiction exceeds the prevalence estimated in the studies themselves. The personality trait most consistently associated with addiction is low self-esteem, though extraversion is associated with more intense use. Women with low self-esteem are the most vulnerable group, and the most commonly associated psychopathological symptom was depression. In short, while the evidence suggests a problem in relation to mobile phone use, the vagueness of the cell phone addiction concept and the poor quality of the studies make it difficult to generalize the results. It is necessary to define and unify criteria with a view to carrying out quality studies that permit appropriate comparisons.