DataGuides are concise and accurate summaries of semistructured databases, enabling schema exploration and improving query processing. Unfortunately, DataGuides can be very expensive to compute, especially for large, cyclic databases. For many DataGuide uses, an ``approximate'' summary of the database's structure can be beneficial yet much cheaper to compute. We summarize several uses of DataGuides and define Approximate DataGuides (ADGs), which relax certain aspects of the DataGuide definition. An ADG allows some inaccuracy yet retains properties that make it useful in numerous situations. The core of the paper presents two general approaches for building ADGs, describing algorithms and experimental results.