Mood disorders, especially major depression and bipolar mania, are among the leading causes of disability worldwide. In clinical practice, the diagnosis of mood disorders is done by the medical experts via multiple observations and by means of questionnaires. This system is however subjective, costly, and cannot meet diagnostic needs given the increasing demand, risking a large population of patients with insufficient care. Increasingly in the last decade, many Artificial Intelligence (AI) and particularly Machine Learning (ML) based solutions were proposed to respond to the urgent need for objective, efficient, and effective mental healthcare decision support systems to assist and reduce the load of the medical experts. However, many of these methods lack properties for being “responsible AI”, namely, interpretability/explainability, algorithmic fairness, and privacy considerations (in both their design and final outputs), thus rendering them useless in real life, especially in the light of recent legal developments. This paper aims to provide an overview on the motivations, recent efforts, and potential future directions for responsible multimodal modeling in mental healthcare.