Stress is the most prevailing and global psychological condition that inevitably disrupts the mood and behavior of individuals. Chronic stress may gravely affect the physical, mental, and social behavior of victims and consequently induce myriad critical human disorders. Herein, a review has been presented where supervised learning (SL) and soft computing (SC) techniques used in stress diagnosis have been meticulously investigated to highlight the contributions, strengths, and challenges faced in the implementation of these methods in stress diagnostic models. A three-tier review strategy comprising of manuscript selection, data synthesis, and data analysis was adopted. The issues in SL strategies and the potential possibility of using hybrid techniques in stress diagnosis have been intensively investigated. The strengths and weaknesses of different SL (Bayesian classifier, random forest, support vector machine, and nearest neighbours) and SC (fuzzy logic, nature-inspired, and deep learning) techniques have been presented to obtain clear insights into these optimization strategies. The effects of social, behavioral, and biological stresses have been highlighted. The psychological, biological, and behavioral responses to stress have also been briefly elucidated. The findings of the study confirmed that different types of data/signals (related to skin temperature, electro-dermal activity, blood circulation, heart rate, facial expressions, etc.) have been used in stress diagnosis. Moreover, there is a potential scope for using distinct nature-inspired computing techniques (Genetic Algorithm, Particle Swarm Optimization, Ant Colony Optimization, Whale Optimization Algorithm, Butterfly Optimization, Harris Hawks Optimizer, and Crow Search Algorithm) and deep learning techniques (Deep-Belief Network, Convolutional-Neural Network, and Recurrent-Neural Network) on multimodal data compiled using behavioral testing, electroencephalogram signals, finger temperature, respiration rate, pupil diameter, galvanic-skin-response, and blood pressure. Likewise, there is a wider scope to investigate the use of SL and SC techniques in stress diagnosis using distinct dimensions such as sentiment analysis, speech recognition, handwriting recognition, and facial expressions. Finally, a hybrid model based on distinct computational methods influenced by both SL and SC techniques, adaption, parameter tuning, and the use of chaos, levy, and Gaussian distribution may address exploration and exploitation issues. However, factors such as real-time data collection, bias, integrity, multi-dimensional data, and data privacy make it challenging to design precise and innovative stress diagnostic systems based on artificial intelligence.