Recent proposals present compression as a cost-effective technique to increase cache and memory capacity and bandwidth. While these proposals show potentials of compression, there are several open questions to adopt these proposals in real systems including the following: (1) Do these techniques work for real-world workloads running for long time? (2) Which application domains would potentially benefit the most from compression? (3) At which level of memory hierarchy should we apply compression: caches, main memory, or both? In this article, our goal is to shed light on some main questions on applicability of compression. We evaluate compression in the memory hierarchy for selected examples from different application classes. We analyze real applications with real data and complete runs of several benchmarks. While simulators provide a pretty accurate framework to study potential performance/energy impacts of ideas, they mostly limit us to a small range of workloads with short runtimes. To enable studying real workloads, we introduce a fast and simple methodology to get samples of memory and cache contents of a real machine (a desktop or a server). Compared to a cycle-accurate simulator, our methodology allows us to study real workloads as well as benchmarks. Our toolset is not a replacement for simulators but mostly complements them. While we can use a simulator to measure performance/energy impact of a particular compression proposal, here with our methodology we can study the potentials with long running workloads in early stages of the design. Using our toolset, we evaluate a collection of workloads from different domains, such as a web server of CS department of UW-Madison for 24h, Google Chrome (watching a 1h-long movie on YouTube), and Linux games (playing for about an hour). We also use several benchmarks from different domains, including SPEC, mobile, and big data. We run these benchmarks to completion. Using these workloads and our toolset, we analyze different compression properties for both real applications and benchmarks. We focus on eight main hypotheses on compression, derived from previous work on compression. These properties (Table 2) act as foundation of several proposals on compression, so performance of those proposals depends very much on these basic properties. Overall, our results suggest that compression could be of general use both in main memory and caches. On average, the compression ratio is ≥2 for 64% and 54% of workloads, respectively, for memory and cache data. Our evaluation indicates significant potential for both cache and memory compression, with higher compressibility in memory due to abundance of zero blocks. Among application domains we studied, servers show on average the highest compressibility, while our mobile benchmarks show the lowest compressibility. For comparing benchmarks with real workloads, we show that (1) it is critical to run benchmarks to completion or considerably long runtimes to avoid biased conclusions, and (2) SPEC benchmarks are good representative of ...