Climate change communication has grown highly complex, polarized, and multilingual, and it is thus in urgent need of sophisticated Natural Language Processing (NLP) methods with the ability to extract sentiment, stance, and emotion in a variety of textual materials. This survey gives a detailed overview of sentiment analysis in climate change, with a history of methodological development of traditionally lexicon-based systems to state-of-the-art deep learning systems and transformer-based large language models. It initially presents the basic terms such as the dimensions of sentiment, the language indicators of climate discussion, and area specific issues such as misinformation, politicization, and framing inherent to a culture. The classical methods of lexicon scoring, statistical machine-learned, and engineered textual features provide interpretability but have problems with ambiguity in context, sarcasm, and complexity of narrative. Deep learning methods such as CNNs on discourse classification and RNN/LSTM models on temporal sentiment changes can achieve much better contextual information but need huge annotated datasets. The survey shows the revolutionary potential of BERT-based and GPT-based models, such as domain adapted versions, such as ClimateBERT, SciBERT, IndoBERT, and multilingual transformers, which can be used to analyze cross-cultural climate communication. The comparative understanding of the issues in the global and Indian environments indicates discrepancies in linguistic forms of expression, political framing, and media ecosystems and stresses a necessity of culturally sensitive sentiment modeling.