Data Warehousing and OLAP (On-Line Analytical Processing) have turned into the key technology for comprehensive data analysis. Originally developed for the needs of decision support in business, data warehouses have proven to be an adequate solution for a variety of non-business applications and domains, such as government, research, and medicine. Analytical power of the OLAP technology comes from its underlying multidimensional data model, which allows users to see data from different perspectives. However, this model displays a number of deficiencies when applied to non-conventional scenarios and analysis tasks. This paper presents an attempt to systematically summarize various extensions of the original multidimensional data model that have been proposed by researchers and practitioners in the recent years. Presented concepts are arranged into a formal classification consisting of fact types, factual and fact-dimensional relationships, and dimension types, supplied with explanatory examples from real-world usage scenarios. Both the static elements of the model, such as types of fact and dimension hierarchy schemes, and dynamic features, such as support for advanced operators and derived elements. We also propose a semantically rich graphical notation called X-DFM that extends the popular Dimensional Fact Model by refining and modifying the set of constructs as to make it coherent with the formal model. An evaluation of our framework against a set of common modeling requirements summarizes the contribution.