This chapter reviews the general least squares variance component estimation (LS-VCE) theory, originally developed by Teunissen (1988), and its adaptability and applicability to different structures of functional and stochastic models, referred to as special cases. Accurate analysis and interpretation of geodetic data is crucial for many geoscience applications. We focus on the implementation of LS-VCE for a range of specific models to enhance the reliability and precision of such analysis. LS-VCE has been extensively applied to various geodetic problems, including Global Navigation Satellite System (GNSS) data processing, noise characterization of time series, and deformation monitoring. We begin with an overview of LS-VCE and its significance in estimating optimal stochastic models. We then investigate specific LS-VCE models, including mixed and conditioned linear models, non-negative LS-VCE, and weighted constraints in stochastic models. We further explain the application of LS-VCE in disjunctive group models, nonlinear functional and stochastic models, hard constraints in functional models, multivariate linear models, and weighted total least squares models. By implementing these LS-VCE models, we aim to provide a reliable framework for future research and applications in geoscience. The methodologies and special models presented in this contribution are expected to contribute significantly to many geodetic fields including GNSS time series analysis, data integration, positioning, and deformation analysis.