We study the multi-user scheduling problem for minimizing the Age of Information (AoI) in cellular wireless networks under stationary and non-stationary regimes. We derive fundamental lower bounds for the scheduling problem and design efficient online policies with provable performance guarantees. In the stationary setting, we consider the AoI optimization problem for a set of mobile users travelling around multiple cells. In this setting, we propose a scheduling policy and show that it is 2-optimal. Next, we propose a new adversarial channel model for studying the scheduling problem in non-stationary environments. For N users, we show that the competitive ratio of any online scheduling policy in this setting is at least Ω(N). We then propose an online policy and show that it achieves a competitive ratio of O(N2). Finally, we introduce a relaxed adversarial model with channel state estimations for the immediate future. We propose a heuristic model predictive control policy that exploits this feature and compare its performance through numerical simulations. © 2020 IEEE.