We present the generalized space-time cube, a descriptive model for visualizations of temporal data. Visualizations are described as operations on the cube, which transform the cube's 3D shape into readable 2D visualizations. Operations include extracting subparts of the cube, flattening it across space or time or transforming the cubes geometry and content. We introduce a taxonomy of elementary space-time cube operations and explain how these operations can be combined and parameterized. The generalized space-time cube has two properties: (1) it is purely conceptual without the need to be implemented, and (2) it applies to all datasets that can be represented in two dimensions plus time (e.g. geo-spatial, videos, networks, multivariate data). The proper choice of space-time cube operations depends on many factors, for example, density or sparsity of a cube. Hence, we propose a characterization of structures within space-time cubes, which allows us to discuss strengths and limitations of operations. We finally review interactive systems that support multiple operations, allowing a user to customize his view on the data. With this framework, we hope to facilitate the description, criticism and comparison of temporal data visualizations, as well as encourage the exploration of new techniques and systems. This paper is an extension of Bach et al.'s (2014) work.