This chapter provides a systematic overview of Data Envelopment Analysis (DEA) and its applications in measuring technical efficiency and total factor productivity (TFP), presenting a complete framework from theoretical foundations to various indices and their extended forms. It begins with Farrell’s concept of efficiency and Shephard’s distance functions, explaining radial models under constant returns to scale (CRS) and variable returns to scale (VRS) assumptions (CCR and BCC models) and their respective applicability. The discussion then extends to non-radial models, including the Russell Measure (RM) and the Slack-Based Measure (SBM) model, as well as SBM variants that handle undesirable outputs, with a systematic comparison between input-oriented and output-oriented approaches. Statistical inference and robustness analysis in DEA models are introduced, and the duality theory is used to interpret shadow prices and other economic meanings. In the productivity analysis section, the chapter details the Malmquist index proposed by Färe et al. (1994b) and its two-factor and three-factor decompositions, compares the FGNZ and Ray–Desli (RD) decompositions, and summarizes multiple extended forms, including the Global Malmquist, Biennial Malmquist, Sequential Malmquist, Meta-frontier Malmquist, as well as the Malmquist–Luenberger (ML) index and Luenberger Productivity Indicator (LPI) for cases involving undesirable outputs. These approaches capture the dynamic processes of technical change and efficiency change and provide stronger comparability in contexts with heterogeneous technologies or environmental constraints. Finally, the chapter illustrates the applicability and extension potential of DEA and various Malmquist indices through typical applications in energy–environment efficiency, regional economic comparisons, and technological convergence, offering a systematic methodological foundation for multidimensional and multi-period efficiency and productivity analysis.