Natural Language Processing (NLP) aims to utilize computational resources to comprehend and generate human language. Emotion and sentiment are integral parts of human beings, and they are often reflected in human language. Consequently, these two closely related ideas are of paramount importance to NLP. In this thesis, we focus on several NLP tasks related to human emotion and sentiment. Particularly, we focus on the domains of Sentiment Analysis and Emotion-Cause Analysis (ECA). Like most other NLP tasks, machine learning technologies are frequently leveraged to perform various NLP tasks in these two domains. A common challenge in applying machine learning technology to context-dependent tasks like Sentiment Analysis is that they require a large amount of labeled data to develop a performant model. In this thesis, we develop several techniques leveraging Transformer-based large language models (LLMs) to perform various NLP tasks within these two domains in a limited to no labeled data setting. Specifically, we devise two technical architectures to perform multi-class Sentiment Analysis with limited labeled data. We introduce two new NLP tasks within the domain of ECA, which are also the first Natural Language Generation (NLG) tasks in this domain. We devise technical solutions to perform these NLG tasks, one with limited labeled data, and the other with no labeled data. We publish a new dataset for one of these novel NLG tasks. Lastly, we propose leveraging conversational LLMs for the automatic evaluation of open-ended NLG tasks, which also does not require any new training or labeled data.