This paper explores how artificial intelligence (AI) technology can contribute to achieve progress on good health and well-being, one of the United Nations' 17 Sustainable Development Goals. It is estimated that one in ten of the global population lived with a mental disorder. Inspired by studies showing that engaging and viewing beautiful natural images can make people feel happier and less stressful, lead to higher emotional well-being, and can even have therapeutic values, we explore how AI can help to promote mental health by developing automatic algorithms for finding beautiful and happy images. We first construct a large image database consisting of nearly 20K very high resolution colour photographs of natural scenes where each image is labelled with beautifulness and happiness scores by about 10 observers. Statistics of the database shows that there is a good correlation between the beautifulness and happiness scores which provides anecdotal evidence to corroborate that engaging beautiful natural images can potentially benefit mental well-being. Building on this unique database, the very first of its kind, we have developed a deep learning based model for automatically predicting the beautifulness and happiness scores of natural images. Experimental results are presented to show that it is possible to develop AI algorithms to automatically assess an image's beautifulness and happiness values which can in turn be used to develop applications for promoting mental health and well-being.