Relevance feedback on search results indicates users' search intent and preferences. Extensive studies have shown that incorporating relevance feedback (RF) on the top k (usually 10) ranked results significantly improves the performance of re-ranking. However, most existing research on user feedback focuses on words-based retrieval models. Recently, neural retrieval models have shown their efficacy in capturing relevance matching in retrieval but little research has been conducted on neural approaches to feedback. This leads us to study different aspects of feedback with neural approaches in the dissertation. RF techniques are seldom used in real search scenarios since they can require significant manual efforts to obtain explicit judgments for search results. However, with mobile or voice-based intelligent assistants being more popular nowadays, user feedback of result quality could be collected potentially during their interactions with the assistants. We study both positive and negative RF to refine the re-ranking performance. Positive feedback aims to find more relevant results given some known relevant results while negative feedback targets identifying the first relevant result. In most cases, it is more beneficial to find the first relevant result compared with finding additional relevant results. However, negative feedback is much more challenging than positive feedback since relevant results are usually similar while non-relevant results could vary considerably. We focus on the tasks of text retrieval and product search to study the different aspects of incorporating feedback for ranking refinement with neural approaches. Our contributions are: (1) we show that iterative relevance feedback (IRF) is more effective than top-k RF on answer passages and we further improve IRF with neural approaches; (2) we propose an effective RF technique based on neural models for product search; (3) we study how to refine re-ranking with negative feedback for conversational product search; (4) we leverage negative feedback in user responses to ask clarifying questions in open-domain conversational search. Our research improves retrieval performance by incorporating feedback in interactive retrieval and approaches multi-turn conversational information-seeking tasks with a focus on positive and negative feedback.