Due to the increasing demands of today's fast-paced world, mental health concerns are on the rise, which necessitates innovative approaches to provide support to those in need. Open-domain conversational agents known as chatbots, offer a unique opportunity to provide empathetic support to individuals struggling with psychological distress. By combining the advancements in natural language processing, such as the advent of large language models and machine learning techniques that can understand human emotions, empathetic chatbots can establish meaningful connections, provide support in distress, and promote mental well-being. This thesis aims to develop empathetic conversational agents that are capable of providing emotional support to people undergoing distress. They are designed in a way such that they offer a reliable space for individuals to express their feelings and motivate them to navigate their emotional challenges and cope with them, ultimately leading to enhanced mental well-being. However, developing such chatbots poses significant challenges such as understanding subtle variations in human emotion, overcoming limitations in training data, ensuring interpretability and reliability of responses, and adhering to established psychological norms and professional tone when responding to distressing situations. In this thesis, we develop resources and methods to address the above challenges and attempt to pave the way for a more compassionate and accessible approach to emotional well-being. To achieve this goal, first, we look at subtle emotional variations present in human conversations and communication strategies humans use to convey empathy, which form the foundation for developing more controllable and interpretable chatbot models that can respond to a wide range of emotions. Then we narrow our attention toward the more challenging task of responding empathetically to extremely negative emotions in psychologically distressing situations. Analyzing dialogues from online peer support forums, we build a knowledge graph that identifies a multitude of distress-related topics and emotionally relieving responses associated with them, facilitating the development of more reliable and topically appropriate chatbot models for distress support. Moving a step further, we analyze the differences in language used by laypersons and professionals when responding to distress and guided by these observations, develop methods to enhance chatbots' professional tone and adherence to therapeutic norms. Overall, this thesis contributes to the advancement of empathetic chatbots that can provide safe, dependable, and professional assistance to users in need.