<p>In the era of big data, machine learning (ML) has become a powerful tool in various scientific and engineering fields, notably impacting structural dynamics. ML algorithms offer advantages by modeling physical phenomena based on data, even in the absence of underlying mechanisms. However, uncertainties such as measurement noise and modeling errors can compromise the reliability of ML predictions, highlighting the need for effective uncertainty awareness to enhance prediction robustness. This paper presents a comprehensive literature survey on navigating uncertainties in ML, categorizing uncertainty-aware approaches into probabilistic methods (including Bayesian and frequentist perspectives) and non-probabilistic methods (such as interval learning and fuzzy learning). Bayesian neural networks, known for their uncertainty quantification and nonlinear mapping capabilities, are emphasized for their superior performance and potential. The survey covers various techniques and methodologies for addressing uncertainties in ML, discussing fundamentals and implementation procedures of each method. While providing a concise overview of fundamental concepts, the paper refrains from in-depth critical explanations. Strengths and limitations of each approach are examined, along with their applications in uncertainty-aware structural dynamics forward problems like response prediction, sensitivity assessment, and reliability analysis, and inverse problems like system identification, model updating, and damage identification. Additionally, the survey identifies research gaps and suggests future directions for investigations, aiming to provide comprehensive insights to the research community. By offering an extensive overview of both probabilistic and non-probabilistic approaches, this survey aims to assist researchers and practitioners in making informed decisions when utilizing ML techniques to address uncertainties in structural dynamics problems.</p>