Based on machine learning, the digital transformation of traditional industries brings a massive data growth, while the intelligent enhancement of products services raises the demand for computing power. Cloud computing, relying on flexible resource deployment, can provide inexpensive and convenient outsourced computing services for users with limited resources, enabling them to complete model training and model hosting for machine learning. It also contributes to the intelligent improvement of products and services and promotes the growth of the digital economy. However, data and model outsourcing come with a transfer of control, which may pose data leakage risk and computational security issues. In recent years, the security issues of machine learning outsourcing have received increasing public attentions and academic concerns. In this paper, we systematically reviewed the research work on machine learning security outsourcing in the year of 2018−2022 the past five years. We first present different outsourced modes, including model training and model hosting modes classified by the task phase, single-cloud and multi-cloud modes classified by the number of cloud service providers. Then we summarize the characteristics of outsourced models under different modes. Next, we focus on the research progress related to machine learning secure outsourced computing from the perspective of typical machine learning algorithms such as logistic regression, Bayesian classification, support vector machine, decision tree and neural network, and provide an in-depth description and analysis. Finally, we analyze and discuss the limitations from different perspectives, as well as potential challenges and opportunities.