File systems store data in files and organize these files in directories. Over decades, file systems have evolved to handle increasingly large files: they distribute files across a cluster of machines, they parallelize access to these files, they decouple data access from metadata access, and hence they provide scalable file access for high-performance applications. Sadly, most cluster-wide file systems lack any sophisticated support for large directories. In fact, most cluster file systems continue to use directories that were designed for humans, not for large-scale applications. The former use-case typically involves hundreds of files and infrequent concurrent mutations in each directory, while the latter use-case consists of tens of thousands of concurrent threads that simultaneously create large numbers of small files in a single directory at very high speeds. As a result, most cluster file systems exhibit very poor file create rate in a directory either due to limited scalability from using a single centralized directory server or due to reduced concurrency from using a system-wide synchronization mechanism. This dissertation proposes a directory architecture called GIGA+ that enables a directory in a cluster file system to store millions of files and sustain hundreds of thousands of concurrent file creations every second. GIGA+ makes two indexing technique to scale out a growing directory on many servers and an efficient layered design to scale up performance. GIGA+ uses a hash-based, incremental partitioning algorithm that enables highly concurrent directory indexing through asynchrony and eventual consistency of the internal indexing state (while providing strong consistency guarantees to the application data). This dissertation analyzes several trade-offs between data migration overhead, load balancing effectiveness, directory scan performance, and entropy of indexing state made by the GIGA+ design, and compares them with policies used in other systems. GIGA+ also demonstrates a modular implementation that separates directory distribution from directory representation. It layers a client-server middleware, which spreads work among many GIGA+ servers, on top of a backend storage system, which manages on-disk directory representation. This dissertation studies how system behavior is tightly dependent on both the indexing scheme and the on-disk implementations, and evaluates how the system performs for different backend configurations including local and shared-disk stores. The GIGA+ prototype delivers highly scalable directory performance (that exceeds the most demanding Petascale-era requirements), provides the traditional UNIX file system interface (that can run applications without any modifications) and offers a new functionality layered on existing cluster file systems (that lack support for distributed directories)contributions: a concurrent