The COVID-19 pandemic has affected millions of people globally, with respiratory organs being strongly affected in individuals with comorbidities. Medical imaging-based diagnosis and prognosis have become increasingly popular in clinical settings for detecting COVID-19 lung infections. Among various medical imaging modalities, ultrasound stands out as a low-cost, mobile, and radiation-safe imaging technology. In this comprehensive review, we focus on AI-driven studies utilizing lung ultrasound (LUS) for COVID-19 detection and analysis. We provide a detailed overview of both publicly available and private LUS datasets and categorize the AI studies according to the dataset they used. Additionally, we systematically analyzed and tabulated the studies across various dimensions, including data preprocessing methods, AI models, cross-validation techniques, and evaluation metrics. In total, we reviewed 60 articles, 41 of which utilized public datasets, while the remaining employed private data. Our findings suggest that ultrasound-based AI studies for COVID-19 detection have great potential for clinical use, especially for children and pregnant women. Our review also provides a useful summary for future researchers and clinicians who may be interested in the field.