The opinion mining and human-agent interaction communities are currently addressing sentiment analysis from different perspectives that comprise, on the one hand, disparate sentiment-related phenomena and computational representations, and on the other hand, different detection and dialog management methods. In this paper we identify and discuss the growing opportunities for cross-disciplinary work that may increase individual advances. Sentiment/opinion detection methods used in human-agent interaction are indeed rare and, when they are employed, they are not different from the ones used in opinion mining and consequently not designed for socio-affective interactions (timing constraint of the interaction, sentiment analysis as an input and an output of interaction strategies). To support our claims, we present a comparative state of the art which analyzes the sentiment-related phenomena and the sentiment detection methods used in both communities and makes an overview of the goals of socio-affective human-agent strategies. We propose then different possibilities for mutual benefit, specifying several research tracks and discussing the open questions and prospects. To show the feasibility of the general guidelines proposed we also approach them from a specific perspective by applying them to the case of the Greta embodied conversational agents platform and discuss the way they can be used to make a more significative sentiment analysis for human-agent interactions in two different use cases: job interviews and dialogs with museum visitors.