Non-invasive methods of detecting heat stress magnitude for livestock is gaining momentum in the context of global climate change. Therefore, the objective of this review is to focus on the synthesis information pertaining to recent efforts to develop heat stress detection systems for livestock based on multiple behavioral and physiological responses. There are a number of approaches to quantify farm animal heat stress response, and from an animal welfare point of view, these can be categorized as invasive and non-invasive approaches. The concept of a non-invasive approach to assess heat stress primarily looks into behavioral and physiological responses which can be monitored without any human interference or additional stress on the animal. Bioclimatic thermal indices can be considered as the least invasive approach to assess and/or predict the level of heat stress in livestock. The quantification and identification of the fecal microbiome in heat-stressed farm animals is one of the emerging techniques which could be effectively correlated with animal adaptive responses. Further, tremendous progress has been made in the last decade to quantify the classical heat stress endocrine marker, cortisol, non-invasively in the feces, urine, hair, saliva and milk of farm animals. In addition, advanced technologies applied for the real-time analysis of cardinal signs such as sounds through microphones, behavioral images, videos through cameras, and data stalking body weight and measurements might provide deeper insights towards improving biological metrics in livestock exposed to heat stress. Infrared thermography (IRT) can be considered another non-invasive modern tool to assess the stress response, production, health, and welfare status in farm animals. Various remote sensing technologies such as ear canal sensors, rumen boluses, rectal and vaginal probes, IRT, and implantable microchips can be employed in grazing animals to assess the quantum of heat stress. Behavioral responses and activity alterations to heat stress in farm animals can be monitored using accelerometers, Bluetooth technology, global positioning systems (GPSs) and global navigation satellite systems (GNSSs). Finally, machine learning offers a scalable solution in determining the heat stress response in farm animals by utilizing data from different sources such as hardware sensors, e.g., pressure sensors, thermistors, IRT sensors, facial recognition machine vision sensors, radio frequency identification, accelerometers, and microphones. Thus, the recent advancements in recording behavior and physiological responses offer new scope to quantify farm animals’ heat stress response non-invasively. These approaches could have greater applications in not only determining climate resilience in farm animals but also providing valuable information for defining suitable and accurate amelioration strategies to sustain their production.