Sarcasm is a form of verbal irony that is often used to express ridicule or contempt. When using sarcasm, a speaker expresses their opinion in an indirect way, where the literal meaning is different from the intended one. Additionally, sarcasm is a sociolinguistic tool that people use to express themselves and it reflects their cultural and social background. Sarcasm detection refers to the process of automatically and computationally identifying whether a piece of text is sarcastic. This has been well studied in the context of English, but Arabic lags behind. In this thesis, we try to fill in the gaps in the research on Arabic sarcasm detection. First, we start by exploring approaches to create an Arabic sarcasm dataset. We create ArSarcasm dataset through the re-annotation of existing sentiment analysis datasets. These labels represent perceived sarcasm as the labels reflect the annotators' perception. The analysis shows that sarcasm is prominent in the used sentiment datasets, with 16% of the sentences being sarcastic. Our experiments show that sarcasm is disruptive for sentiment analysers. Analysis shows that annotating subjective content can be challenging and prone to biases. Second, to mitigate the issues and fallbacks of sarcasm data collection approaches, we propose to collect sarcasm datasets by asking people to label their words, which is referred to as intended sarcasm. The resulting dataset, which is first-party annotated, would have more reliable and trustworthy labels and does not have the issues of third-party annotated data. Next, we test state-of-the-art machine learning models on the newly created datasets. Those experiments provide a benchmark for these datasets. The experiments show that intended sarcasm detection is more challenging than perceived sarcasm detection. Also, the experiments show that monolingual Arabic language models, which include dialects in their pre-training data, perform better on the sarcasm detection task. Additionally, we provide the details of shared tasks that utilise the new datasets. Finally, we provide an in-depth error analysis comparing humans' performance in sarcasm detection against the performance of state-of-the-art models. Our analysis confirms that sarcasm is challenging for both humans and machines. We also highlight the features and patterns used to express sarcasm, such as idioms and proverbs. When extending the analysis to focus on Arabic dialects, we found that dialect familiarity affects how Arabic speakers understand and interpret sarcasm. Arabic speakers were better able to detect sarcasm expressed in their dialect or one they were familiar with.