A mix network (mixnet) is a routing network that conceals communication patterns by shuffling, or mixing, the routes of concurrently transmitted messages, thereby providing anonymity for senders, receivers, and sender-receiver pairs. Notable examples of deployed mixnets are Tor and Nym. Given the potential use of mixnets in high-stakes applications, such as protecting whistleblowers, it is essential to establish formal guarantees of sender anonymity, even against powerful adversaries that have a full view of the network and are capable of compromising subsets of mix servers. However, existing analyses of mixnets anonymity typically rely on additional mechanisms, such as noise or chaff messages, or are based on empirical metrics such as entropy, which cannot provide strong guarantees in the presence of adversaries with auxiliary information. My thesis consists of two complementary parts: (1) a first part on parallel mixnets, in which mix nodes operate in loosely synchronized rounds, and (2) a second part on continuous-time mixnets, in which mix nodes operate independently and forward messages after user-specified random delays. First, I present a new analysis of horizontally scalable parallel mixnets, showing that they can achieve strong indistinguishability guarantees for messages without requiring additional noise messages or extensive cryptographic techniques. Second, I develop a theoretical framework for continuous-time mixing by identifying two interacting stochastic processes that govern mixnets' operation: a local shuffling process at each mix node, driven by message delays and their sampling, and a global shuffling process that determines how messages (or batches) propagate between mixing layers. Building on this perspective, I derive a new tractable analytical model that captures mixing at both the local (per-node) and global (system-wide) levels. Finally, I use this model to establish provable anonymity guarantees for asynchronous mixnets.