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For around a decade, deep learning - the sub-field of machine learning that refers to artificial neural networks comprised of many computational layers - modifies the landscape of statistical model development in many research areas, such as image classification, machine translation, and speech recognition. Geoscientific disciplines in general and the field of hydrology in particular, also do not stand aside from this movement. Recently, the proliferation of modern deep learning-based techniques and methods has been actively gaining popularity for solving a wide range of hydrological problems: modeling and forecasting of river runoff, hydrological model parameters regionalization, assessment of available water resources. identification of the main drivers of the recent change in water balance components. This growing popularity of deep neural networks is primarily due to their high universality and efficiency. The presented qualities, together with the rapidly growing amount of accumulated environmental information, as well as increasing availability of computing facilities and resources, allow us to speak about deep neural networks as a new generation of mathematical models designed to, if not to replace existing solutions, but significantly enrich the field of geophysical processes modeling. This paper provides a brief overview of the current state of the field of development and application of deep neural networks in hydrology. Also in the following study, the qualitative long-term forecast regarding the development of deep learning technology for managing the corresponding hydrological modeling challenges is provided based on the use of "Gartner Hype Curve", which in the general details describes a life cycle of modern technologies.