Performing automatic reformulations of a user's query is a popular paradigm used in information retrieval (IR) for improving effectiveness -- as exemplified by the pseudo-relevance feedback approaches, which expand the query in order to alleviate the vocabulary mismatch problem. Recent advancements in generative language models have demonstrated their ability in generating responses that are relevant to a given prompt. In light of this success, we seek to study the capacity of such models to perform query reformulation and how they compare with long-standing query reformulation methods that use pseudo-relevance feedback. In particular, we investigate two representative query reformulation frameworks, GenQR and GenPRF. GenQR directly reformulates the user's input query, while GenPRF provides additional context for the query by making use of pseudo-relevance feedback information. For each reformulation method, we leverage different techniques, including fine-tuning and direct prompting, to harness the knowledge of language models. The reformulated queries produced by the generative models are demonstrated to markedly benefit the effectiveness of a state-of-the-art retrieval pipeline on four TREC test collections (varying from TREC 2004 Robust to the TREC 2019 Deep Learning). Furthermore, our results indicate that our studied generative models can outperform various statistical query expansion approaches while remaining comparable to other existing complex neural query reformulation models, with the added benefit of being simpler to implement.