The field of Natural Language Processing (NLP) has witnessed a surging interest in the elusive realm of humour detection. Humour, deeply rooted in the human experience, has posed a unique challenge for computational systems. Researchers have embarked on diverse endeavours to computationally recognize humour, ranging from the exploration of wordplay within jokes to the identification of humorous texts and satire in social media. These studies span a spectrum of methodologies and approaches, incorporating theories of humour, linguistic and semantic features and machine-learning techniques. From the computational recognition of wordplay through Raskin's theory of humour to the employment of word-association-based semantic features that surpass traditional methods, the research landscape is rich and diverse. Generative language models and pre-trained language models, such as BERT and Transformer architectures, play pivotal roles in this domain, offering novel avenues for humour detection. Furthermore, comparative studies explore the intersection of irony detection and established humour classification techniques, shedding light on their efficacy. This diverse array of methodologies and models collectively contributes to the evolving field of humour detection using NLP.