In the current era, people and society have grown increasingly reliant on artificial intelligence (AI) technologies. AI has the potential to drive us towards a future in which all of humanity flourishes. It also comes with substantial risks for oppression and calamity. Discussions about whether we should (re)trust AI have repeatedly emerged in recent years and in many quarters, including industry, academia, healthcare, services, and so on. Technologists and AI researchers have a responsibility to develop trustworthy AI systems. They have responded with great effort to design more responsible AI algorithms. However, existing technical solutions are narrow in scope and have been primarily directed towards algorithms for scoring or classification tasks, with an emphasis on fairness and unwanted bias. To build long-lasting trust between AI and human beings, we argue that the key is to think beyond algorithmic fairness and connect major aspects of AI that potentially cause AI’s indifferent behavior. In this survey, we provide a systematic framework of Socially Responsible AI Algorithms that aims to examine the subjects of AI indifference and the need for socially responsible AI algorithms, define the objectives, and introduce the means by which we may achieve these objectives. We further discuss how to leverage this framework to improve societal well-being through protection, information, and prevention/mitigation.