Graph databases have gained renewed interest in the last years, due to its applications in areas such as the Semantic Web and Social Networks Analysis. We study the problem of querying graph databases, and, in particular, the expressiveness and complexity of evaluation for several general-purpose query languages, such as the regular path queries and its extensions with conjunctions and inverses. We distinguish between two semantics for these languages. The first one, based on simple paths, easily leads to intractability, while the second one, based on arbitrary paths, allows tractable evaluation for an expressive family of languages.We also study two recent extensions of these languages that have been motivated by modern applications of graph databases. The first one allows to treat paths as first-class citizens, while the second one permits to express queries that combine the topology of the graph with its underlying data.