Advanced measurement and data storage technologies have enabled high-dimensional profiling of complex biological systems. For this, modern multiomics studies regularly produce datasets with hundreds of thousands of measurements per sample, enabling a new era of precision medicine. Correlation analysis is an important first step to gain deeper insights into the coordination and underlying processes of such complex systems. However, the construction of large correlation networks in modern high-dimensional datasets remains a major computational challenge owing to rapidly growing runtime and memory requirements. Here we address this challenge by introducing CorALS (Correlation Analysis of Large-scale (biological) Systems), an open-source framework for the construction and analysis of large-scale parametric as well as non-parametric correlation networks for high-dimensional biological data. It features off-the-shelf algorithms suitable for both personal and high-performance computers, enabling workflows and downstream analysis approaches. We illustrate the broad scope and potential of CorALS by exploring perspectives on complex biological processes in large-scale multiomics and single-cell studies.