Drought is one of the major stress factors affecting the growth and development of plants. In this context, drought-related losses of crop plant productivity impede sustainable agriculture all over the world. In general, plants respond to water deficits by multiple physiological and metabolic adaptations at the molecular, cellular, and organism levels. To understand the underlying mechanisms of drought tolerance, adequate stress models and arrays of reliable stress markers are required. Therefore, in this review we comprehensively address currently available models of drought stress, based on culturing plants in soil, hydroponically, or in agar culture, and critically discuss advantages and limitations of each design. We also address the methodology of drought stress characterization and discuss it in the context of real experimental approaches. Further, we highlight the trends of methodological developments in drought stress research, i.e., complementing conventional tests with quantification of phytohormones and reactive oxygen species (ROS), measuring antioxidant enzyme activities, and comprehensively profiling transcriptome, proteome, and metabolome.