Since the introduction of cost-based query optimization by Selinger et al. in their seminal paper, the performance-critical role of interesting orders has been recognized. Some algebraic operators change interesting orders (e.g. sort and select), while others exploit them (e.g. merge join). Likewise, Wang and Cherniack (VLDB 2003) showed that existing groupings should be exploited to avoid redundant grouping operations. Ideally, the reasoning about interesting orderings and groupings should be integrated into one framework.So far, no complete, correct, and efficient algorithm for ordering and grouping inference has been proposed. We fill this gap by proposing a general two-phase approach that efficiently integrates the reasoning about orderings and groupings. Our experimental results show that with a modest increase of the time and space requirements of the preprocessing phase both orderings and groupings can be handled at the same time. More importantly, there is no additional cost for the second phase during which the plan generator changes and exploits orderings and groupings by adding operators to subplans.