Cooperation between the primary and secondary systems can improve the spectrum efficiency in cognitive radio networks. The key idea is that the secondary system helps to boost the primary system's performance by relaying, and, in return, the primary system provides more opportunities for the secondary system to access the spectrum. In contrast to most of existing works that only consider information cooperation, this paper studies joint information and energy cooperation between the two systems, i.e., the primary transmitter sends information for relaying and feeds the secondary system with energy as well. This is particularly useful when the secondary transmitter has good channel quality to the primary receiver but is energy constrained. We propose and study three schemes that enable this cooperation. First, we assume there exists an ideal backhaul between the two systems for information and energy transfer. We then consider two wireless information and energy transfer schemes from the primary transmitter to the secondary transmitter using power splitting and time splitting energy harvesting techniques, respectively. For each scheme, the optimal and zero-forcing solutions are derived. Simulation results demonstrate promising performance gain for both systems due to the additional energy cooperation. It is also revealed that the power splitting scheme can achieve larger rate region than the time splitting scheme when the efficiency of the energy transfer is sufficiently large