Climate change has a significant impact on winter wheat (Triticum aestivum L.) cultivation due to the occurrence of various environmental stress parameters. It destabilizes wheat production mainly through abiotic stresses (heat waves, drought, floods, frost, salinity, and nutrient deficiency) and improved conditions for pest and disease development and infestation as biotic parameters. The impact of these parameters can be reduced by timely and appropriate management measures such as irrigation, fertilization, or pesticide application. However, this requires the early diagnosis and quantification of the various stressors. Since they induce specific physiological responses in plant cells, structures, and tissues, environmental stress parameters can be monitored by different sensing methods, taking into account that these responses affect the signal in different regions of the electromagnetic spectrum (EM), especially visible (VIS), near infrared (NIR), and shortwave infrared (SWIR). This study reviews recent findings in the application of remote and proximal sensing methods for early detection and evaluation of abiotic and biotic stress parameters in crops, with an emphasis on winter wheat. The study first provides an overview of climate-change-induced stress parameters in winter wheat and their physiological responses. Second, the most promising non-invasive remote sensing methods are presented, such as airborne and satellite multispectral (VIS and NIR) and hyperspectral imaging, as well as proximal sensing methods using VNIR-SWIR spectroscopy. Third, data analysis methods using vegetation indices (VI), chemometrics, and various machine learning techniques are presented, as well as the main application areas of sensor-based analysis, namely, decision-making processes in precision agriculture.