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Conventional design of wireless networks mainly focuses on system capacity and spectral efficiency (SE). As green radio (GR) becomes an inevitable trend, energy-efficient design is becoming more and more important. In this paper, the fundamental tradeoff between energy efficiency (EE) and SE in downlink orthogonal frequency division multiple access (OFDMA) networks is addressed. We first set up a general EE-SE tradeoff framework, where the overall EE, SE and per-user quality-of-service (QoS) are all considered, and prove that under this framework, EE is strictly quasiconcave in SE. We then discuss some basic properties, such as the impact of channel power gain and circuit power on the EE-SE relation. We also find a tight upper bound and a tight lower bound on the EE-SE curve for general scenarios, which reflect the actual EE-SE relation. We then focus on a special case that priority and fairness are considered and suggest an alternative upper bound, which is proved to be achievable for flat fading channels. We also develop a low-complexity but near-optimal resource allocation algorithm for practical application of the EE-SE tradeoff. Numerical results confirm the theoretical findings and demonstrate the effectiveness of the proposed resource allocation scheme for achieving a flexible and desirable tradeoff between EE and SE.