The cloud of Linked Open Data is steadily growing, yet it remains largely inaccessible to the general public, due to the technical barrier posed by the requirement to know formal query languages. In this thesis, we present new approaches for visual query formulation toward arbitrary SPARQL endpoints. Class hierarchies appear naturally in many such datasets. To support these cases, we assess different approaches for supporting subclass reasoning in SPARQL queries, and show how subclass hierarchies can be integrated in visual search tools. We present five different alternatives for supporting subclass reasoning: RDFS backward reasoning, RDFS forward reasoning, property paths, query rewriting, and query federation. The technical details of our suggested approaches for supporting subclass reasoning are thoroughly discussed with a case study drawn from the Norwegian Entity Registry. The performance of each approach is measured in a benchmarking experiment, where RDFS reasoning and query rewriting is found to perform well, while the property paths and query federation approaches are found to be inadequate for supporting subclass reasoning. We present two visual search tool prototypes for Linked Open Data, developed to improve the accessibility to Linked Open Data sources for casual users, and we show how subclass hierarchies can be integrated in these tools. The usability of our suggested subclass integration is assessed in a user study, where it is shown to perform adequately.