Secure messaging applications are used by billions of users every day. Applications like WhatsApp make use of the seminal Signal protocol that provides conversation participants with end-to-end encryption guarantees. Due to the long-lived nature of messaging sessions, the threat of state exposure is more pronounced, and thus protocols like Signal regularly refresh keying material. In the cryptographic literature, many works address possible performance/security trade-offs beyond Signal and address additional problems like providing security against bad randomness generators and detecting active attacks. In this presentation, we examine this exciting line of work, discuss ongoing work and propose directions for further research. In particular we consider both the two-party setting and the more challenging group setting where parties may join and leave a group over time.