The tunneling current between independently contacted graphene sheets separated by boron nitride insulator is calculated. Both dissipative tunneling transitions, with momentum transfer due to disorder scattering, and non-dissipative regime of tunneling, which appears due to intersection of electron and hole branches of energy spectrum, are described. Dependencies of tunneling current on concentrations in top and bottom graphene layers, which are governed by the voltages applied through independent contacts and gates, are considered for the back- and double-gated structures. The current-voltage characteristics of the back-gated structure are in agreement with the recent experiment [Science 335, 947 (2012)]. For the double-gated structures, the resonant dissipative tunneling causes a ten times enhancement of response which is important for transistor applications.
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