Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. In this paper, we present a deep theoretical analysis of threshold query evaluation and show that thresholds can be used to significantly improve the asymptotic bounds of state-of-the-art query evaluation algorithms. We also empirically show that threshold queries are significant in practice. In surprising contrast to conventional wisdom, we found important scenarios in real-world data sets in which users are interested in computing the results of queries up to a certain threshold, independent of a ranking function that orders the query results.