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The FuzzyLog is a partially ordered shared log abstraction. Distributed applications can concurrently append to the partial order and play it back. FuzzyLog applications obtain the benefits of an underlying shared log – extracting strong consistency, durability, and failure atomicity in simple ways – without suffering from its drawbacks. By exposing a partial order, the FuzzyLog enables three key capabilities for applications: linear scaling for throughput and capacity (without sacrificing atomicity), weaker consistency guarantees, and tolerance to network partitions. We present Dapple, a distributed implementation of the FuzzyLog abstraction that stores the partial order compactly and supports efficient appends / playback via a new ordering protocol. We implement several data structures and applications over the FuzzyLog, including several map variants as well as a ZooKeeper implementation. Our evaluation shows that these applications are compact, fast, and flexible: they retain the simplicity (100s of lines of code) and strong semantics (durability and failure atomicity) of a shared log design while exploiting the partial order of the Fuzzy-Log for linear scalability, flexible consistency guarantees (e.g., causal+ consistency), and network partition tolerance. On a 6-node Dapple deployment, our FuzzyLog- based ZooKeeper supports 3M/sec single-key writes, and 150K/sec atomic cross-shard renames.