Query expansion is an important and commonly used technique for improving Web search results. Existing methods for query expansion have mostly relied on global or local analysis of document collection, click-through data, or simple ontologies such as WordNet. In this paper, we present the results of a systematic study of the methods leveraging the ConceptNet knowledge base, an emerging new Web resource, for query expansion. Specifically, we focus on the methods leveraging ConceptNet to improve the search results for poorly performing (or difficult) queries. Unlike other lexico-semantic resources, such as WordNet and Wikipedia, which have been extensively studied in the past, ConceptNet features a graph-based representation model of commonsense knowledge, in which the terms are conceptually related through rich relational ontology. Such representation structure enables complex, multi-step inferences between the concepts, which can be applied to query expansion. We first demonstrate through simulation experiments that expanding queries with the related concepts from ConceptNet has great potential for improving the search results for difficult queries. We then propose and study several supervised and unsupervised methods for selecting the concepts from ConceptNet for automatic query expansion. The experimental results on multiple data sets indicate that the proposed methods can effectively leverage ConceptNet to improve the retrieval performance of difficult queries both when used in isolation as well as in combination with pseudo-relevance feedback.