This survey paper offers a comprehensive review of the recent advances and applications of Machine Learning (ML) approaches in the interdisciplinary field of bioengineering, specifically in the realm of biosignal processing. Biosignals, including electroencephalograms (EEG), electrocardiograms (ECG), and electromyograms (EMG), are inherently complex, presenting significant challenges such as noise, artifacts, variability, and nonlinearity in their processing. However, ML has shown promise in overcoming these hurdles, enabling the extraction of useful features and insights from these signals. The paper outlines how ML is leveraged for processing, analyzing, classifying, and interpreting biosignals for various applications, such as diagnosis, monitoring, rehabilitation, and brain-computer interfaces. Additionally, it discusses the ongoing challenges and potential future directions of ML applications in this field. Through this review, we aim to highlight the critical role of ML in enabling adaptive, personalized, and intelligent systems that interact with biosignals in real-time, with potential implications for improving patient outcomes in various medical conditions.