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In this paper, we focus on verifiability of predicate encryption. A verifiable predicate encryption scheme guarantees that all legitimate receivers of a ciphertext will obtain the same message upon decryption. While verifiability of predicate encryption might be a desirable property by itself, we furthermore show that this property enables interesting applications. Specifically, we provide two applications of verifiable predicate encryption. Firstly, we show that for a large class of verifiable predicate encryption schemes, it is always possible to convert a chosen-plaintext secure scheme into a chosen-ciphertext secure one. Secondly, we show that a verifiable predicate encryption scheme allows the construction of a deniable predicate authentication scheme . This primitive enables a user to authenticate a message to a verifier using a private key satisfying a specified relation while at the same time allowing the user to deny ever having interacted with the verifier. This scheme furthermore guarantees the anonymity of the user in the sense that the verifier will learn nothing about the user's private key except that it satisfies the specified relation. Lastly, we show that many currently known predicate encryption schemes already provide verifiability, and furthermore demonstrate that many predicate encryption schemes which do not provide verifiability, can be easily converted into schemes providing verifiability. Our results not only highlight that verifiability is a very useful property of predicate encryption, but also show that efficient and practical schemes with this property can be obtained relatively easily.