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The proliferation of mobile users with an attendant rise in energy consumption mainly at the base station has requested new ways of achieving energy efficiency in cellular networks. Many approaches have been proposed to reduce the power consumption at the base stations in response to the contribution of energy cost to the increase of OPEX of the mobile operators and the rise of the carbon footprint on global climate. As a springboard to the application of sleep mode methods in ultra-dense cellular networks, this paper provides a comprehensive survey of the base station sleep mode strategies in heterogeneous mobile networks from perspectives of modeling and algorithm design. Specifically, the sleep mode enabling strategies and sleep wake-up schemes are reviewed. The base station sleep-mode techniques in ultra-dense networks are further discussed as well as the challenges and possible solutions.