Ecological networks of species interactions are popular and provide powerful analytical tools for understanding variation in community structure and ecosystem functioning. However, network analyses and commonly used metrics such as nestedness and connectance have also attracted criticism. One major concern is that observed patterns are misinterpreted as niche properties such as specialization, whereas they may instead merely reflect variation in sampling, abundance, and/or diversity. As a result, studies potentially draw flawed conclusions about ecological function, stability, or coextinction risks. We highlight potential biases in analyzing and interpreting species-interaction networks and review the solutions available to overcome them, among which we particularly recommend the use of null models that account for species abundances. We show why considering variation across species and networks is important for understanding species interactions and their consequences. Network analyses can advance knowledge on the principles of species interactions but only when judiciously applied.