The substantial growth of Internet-of-Things technology and the ubiquity of smartphone devices has increased the public and industry focus on speech emotion recognition (SER) technologies. Yet, conceptual, technical, and societal challenges restrict the wide adoption of these technologies in various domains, including, healthcare, and education. These challenges are amplified when automated emotion recognition systems are called to function “in-the-wild” due to the inherent complexity and subjectivity of human emotion, the difficulty of obtaining reliable labels at high temporal resolution, and the diverse contextual and environmental factors that confound the expression of emotion in real life. In addition, societal and ethical challenges hamper the wide acceptance and adoption of these technologies, with the public raising questions about user privacy, fairness, and explainability. This article briefly reviews the history of affective speech processing, provides an overview of current state-of-the-art approaches to SER, and discusses algorithmic approaches to render these technologies accessible to all, maximizing their benefits and leading to responsible human-centered computing applications.