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Sigma-delta modulation techniques have been widely used in moderate and high accuracy analog/mixed-signal IC applications, such as analog-to-digital data converters (ADCs), digital-to-analog data converters (DACs), frequency synthesis, and power amplification. This paper reviews recent progress and advances in sigma-delta modulation designs with a focus on low power solutions. Discrete-time and continuous-time sigma-delta modulators are compared to highlight the power advantages and design challenges in the continuous-time approaches. A low power continuous-time sigma-delta modulator IC design is used to elucidate the tradeoff considerations and the design insights.