Clarifying the robustness of authenticated encryption (AE) schemes, such as security under nonce misuse or Release of Unverified Plaintext (RUP), has significant importance due to the extensive use of AEs in real-world applications. We present a comprehensive analysis of the robustness of well-known standards, namely GCM, CCM, and OCB3. Despite many existing studies, we uncovered several robustness properties for them that were not known in the literature. In particular, we show that both GCM and CCM maintain authenticity under RUP. Moreover, CCM keeps this feature even if a nonce is misused. We show that this robust security is maintained if one block cipher call in CCM is omitted, resulting in an efficiency improvement of CCM since the proposal. Together with existing analysis, our work gives a complete picture of the robustness of these standards for the first time. Our results also imply several new robust AE schemes based on GCM and CCM.