The emergence and evolution of Local Differential Privacy (LDP) and its various adaptations play a pivotal role in tackling privacy issues related to the vast amounts of data generated by intelligent devices, which are crucial for data-informed decision-making in the realm of crowdsensing. Utilizing these extensive datasets can provide critical insights but also introduces substantial privacy concerns for the individuals involved. LDP, noted for its decentralized framework, excels in providing strong privacy protection for individual users during the stages of data collection and processing. The core principle of LDP lies in its technique of altering each user's data locally at the client end before it is sent to the server, thus preventing privacy violations at both stages. There are many LDP variances in the privacy research community aimed to improve the utility-privacy tradeoff. On the other hand, one of the major applications of the privacy-preserving mechanisms is machine learning. In this paper, we firstly delves into a comprehensive analysis of LDP and its variances, focusing on their various models, the diverse range of its adaptations, and the underlying structure of privacy mechanisms; then we discuss the state-of-art privacy mechanisms applications in machine learning.