A systematic approach to solve seemingly nonconvex resource allocation problems in wireless cellular networks is studied in this paper. By revealing and exploiting the hidden convexity in the problem formulations, we obtain solutions that can tackle a variety of objective functions, provide robustness to resource allocations such as power, and be obtained often through distributed algorithms. The advantages of such flexibility and robustness are demonstrated through comparisons with the state-of-the-art in recent research literature. First we show how to distributively solve a variety of resource allocation problems in FDMA and interference limited CDMA channels with quality of service constraints, such as meeting minimum queueing delay or energy per bit requirement. Then, for uplink transmission in a CDMA cellular network, we propose an optimal power control scheme with congestion-aware active link protection. In particular, the tradeoff between power expenditure and the protection margin of the SIR-balancing power algorithm is optimized.