Abstract: As cloud computing technology advances continuously, there are a growing number of enterprises and organizations choosing the inter-cloud approach to apply on IT delivery. Inter-cloud environments can efficiently solve problems such as low resource utilization, resource limitation, and vendor lock-in in traditional single-cloud environments, and manage cloud resources in an integrated model. Due to the heterogeneity of resources in the inter-cloud environment, which will complicate the scheduling of inter-cloud tasks. Based on the current status, how to logically schedule user tasks and allocate them to the most suitable inter-cloud resources for execution has developed to be an important issue to be solved in the inter-cloud environment. From the perspective of the inter-cloud environment, we discuss the progress and future challenges of research on the task of scheduling algorithms under this environment. Firstly, combined with the characteristics of an inter-cloud environment, cloud computing is divided into federated cloud and multi-cloud environments and introduced in detail. Meanwhile, the existing task scheduling types are reviewed and their advantages and disadvantages are analyzed. Secondly, based on the classification and current research procedure, representative documents are selected to analyze the algorithms for task scheduling on inter-cloud. Finally, shortcomings in research on algorithms for task scheduling in inter-cloud and future research trends are discussed, which provide a reference for further research on inter-cloud task scheduling.