The primary goal of today's search and browsing techniques is to find relevant documents. As the current web evolves into the next generation termed the Semantic Web, the emphasis will shift from finding documents to finding facts, actionable information, and insights. Improving ability to extract facts, mainly in the form of entities, embedded within documents leads to the fundamental challenge of discovering relevant and interesting relationships amongst the entities that these documents describe. Relationships are fundamental to semantics-to associate meanings to words, terms and entities. They are a key to new insights. Knowledge discovery is also about discovery of heretofore new relationships. The Semantic Web seeks to associate annotations (i.e., metadata), primarily consisting of based on concepts (often representing entities) from one or more ontologies/vocabularies with all Web-accessible resources such that programs can associate "meaning with data". Not only it supports the goal of automatic interpretation and processing (access, invoke, utilize, and analyze), it also enables improvements in scalability compared to approaches that are not semantics-based. Identification, discovery, validation and utilization of relationships (such as during query evaluation), will be a critical computation on the Semantic Web. Based on our research over the last decade, this paper takes an empirical look at various types of simple and complex relationships, what is captured and how they are represented, and how they are identified, discovered or validated, and exploited. These relationships may be based only on what is contained in or directly derived from data (direct content based relationships), or may be based on information extraction, external and prior knowledge and user defined computations (content descriptive relationships). We also present some recent techniques for discovering indirect (i.e., transitive) and virtual (i.e., user-defined) yet meaningful (i.e., contextually relevant) relationships based on a set of patterns and paths between entities of interest. In particular, we will discuss modeling, representation and computation or validation of three types of complex semantic relationships: (a) using predefined multi-ontology relationships for query processing and corresponding the issue of "loss of information" investigated in the OBSERVER project, (b) rho (Rho) operator for semantic associations which seeks to discover contextually relevant and relevancy ranked indirect relationships or paths between entities using semantic metadata and relevant knowledge, and (c) IScapes which allows interactive, human-directed knowledge validation of hypothesis involving user-defined relationships and operations in a multi-ontology, and multi-agent InfoQuilt system. Representing, identifying, discovering, validating and exploiting complex relationships are important issues related to realizing the full power of the Semantic Web, and can help close the gap between highly separated information retrieval and decision-making steps.