We define two complementary approaches to monitor decentralized systems. The first relies on those with a centralized specification, i.e, when the specification is written for the behavior of the entire system. To do so, our approach introduces a data-structure that i) keeps track of the execution of an automaton, ii) has predictable parameters and size, and iii) guarantees strong eventual consistency. The second approach defines decentralized specifications wherein multiple specifications are provided for separate parts of the system. We study decentralized monitorability, and present a general algorithm for monitoring decentralized specifications. We map three existing algorithms to our approaches and provide a framework for analyzing their behavior. Lastly, we introduce our tool, which is a framework for designing such decentralized algorithms, and simulating their behavior.