O ne effective means to hedge against uncertainty and better match supply with demand in a swiftly changing environment is to adopt a flexible operations strategy that allows timely response to realized demand. The notion of flexible processes and operations has led to significant impact on the performance of many manufacturing and service applications. However, investing a fully flexible system is usually prohibitively expensive with overwhelming implementation complexity and overhead. As a result, the search for efficient system designs with only a limited amount of flexibility but can capture the majority of the benefits achieved by a fully flexible system has been an active research question in the operations literature. Fortunately, it has been widely observed that even just a small amount of flexibility, if configured in a right way, can be extremely effective in hedging against demand uncertainty and mitigating supply-demand mismatch. In this review, we shall present and discuss some recent developments in flexible operations over the past decade. We organize our review into models with independent and dependent capacity allocation decisions across time periods. In the former setting, capacity allocation decisions in one period do not affect future demand fulfillment decisions and one can start over every period as if one is dealing with a single-period model, whereas in the latter case capacity allocation decisions in one period would have an impact on the decisions in future periods. The review concludes with some discussions about topics for future research exploration.