Key-value stores are everywhere. They power a diverse set of data-driven applications across both industry and science. Key-value stores are used as stand-alone NoSQL systems but they are also used as a part of more complex pipelines and systems such as machine learning and relational systems. In this tutorial, we survey the state-of-the-art approaches on how the core storage engine of a key-value store system is designed. We focus on several critical components of the engine, starting with the core data structures to lay out data across the memory hierarchy. We also discuss design issues related to caching, timestamps, concurrency control, updates, shifting workloads, as well as mixed workloads with both analytical and transactional characteristics. We cover designs that are read-optimized, write-optimized as well as hybrids. We draw examples from several state-of-the-art systems but we also put everything together in a general framework which allows us to model storage engine designs under a single unified model and reason about the expected behavior of diverse designs. In addition, we show that given the vast number of possible storage engine designs and their complexity, there is a need to be able to describe and communicate design decisions at a high level descriptive language and we present a first version of such a language. We then use that framework to present several open challenges in the field especially in terms of supporting increasingly more diverse and dynamic applications in the era of data science and AI, including neural networks, graphs, and data versioning.