Human social relationships imply conforming to the norms, behaviors and cultural values of the society, but also socialization of emotions, to learn how to interpret and show them. In multiagent systems, much progress has been made in the analysis and interpretation of both emotions and norms. Nonetheless, the relationship between emotions and norms has hardly been considered and most normative agents do not consider emotions, or vice-versa. In this article, we provide an overview of relevant aspects within the area of normative agents and emotional agents. First we focus on the concept of norm, the different types of norms, its life cycle and a review of multiagent normative systems. Secondly, we present the most relevant theories of emotions, the life cycle of an agent's emotions, and how emotions have been included through computational models in multiagent systems. Next, we present an analysis of proposals that integrate emotions and norms in multiagent systems. From this analysis, four relationships are detected between norms and emotions, which we analyze in detail and discuss how these relationships have been tackled in the reviewed proposals. Finally, we present a proposal for an abstract architecture of a Normative Emotional Agent that covers these four norm-emotion relationships.