<p>Modern big data computing faces fundamental scalability challenges due to the high memory, communication, and computational requirements that grow with data volume. The random sample partition (RSP) model overcomes these constraints through an innovative distributed data representation that organizes large datasets as collections of ready-to-use random samples and enables efficient approximate big data computing with existing sequential algorithms. In this survey, we provide a comprehensive overview of approximate big data computing with the RSP model. We first summarize the foundational concepts and algorithms behind the RSP model. Next, we explore how RSP has been leveraged in big data exploration and analysis, demonstrating its adaptability across various data science and machine learning tasks. We then examine RSP-based big data computing, including the Non-MapReduce computing approach, and its implementation in the LOGO distributed framework. Additionally, we discuss application scenarios like geo-distributed big data analysis in computing power networks and key research challenges with modern workloads and computing paradigms. This work serves both as a foundational reference on the RSP model and as a research agenda for developing next-generation, resource-efficient big data systems.</p>