Worldwide, population aging and unhealthy lifestyles have increased the incidence of high-risk health conditions such as cardiovascular diseases, sleep apnea, and other conditions. Recently, to facilitate early identification and diagnosis, efforts have been made in the research and development of new wearable devices to make them smaller, more comfortable, more accurate, and increasingly compatible with artificial intelligence technologies. These efforts can pave the way to the longer and continuous health monitoring of different biosignals, including the real-time detection of diseases, thus providing more timely and accurate predictions of health events that can drastically improve the healthcare management of patients. Most recent reviews focus on a specific category of disease, the use of artificial intelligence in 12-lead electrocardiograms, or on wearable technology. However, we present recent advances in the use of electrocardiogram signals acquired with wearable devices or from publicly available databases and the analysis of such signals with artificial intelligence methods to detect and predict diseases. As expected, most of the available research focuses on heart diseases, sleep apnea, and other emerging areas, such as mental stress. From a methodological point of view, although traditional statistical methods and machine learning are still widely used, we observe an increasing use of more advanced deep learning methods, specifically architectures that can handle the complexity of biosignal data. These deep learning methods typically include convolutional and recurrent neural networks. Moreover, when proposing new artificial intelligence methods, we observe that the prevalent choice is to use publicly available databases rather than collecting new data.