This chapter provides a practical guide to wavelet analysis, focusing on time series analysis of the El Niño–Southern Oscillation (ENSO). It includes a comparison with the windowed Fourier transform, selection of appropriate wavelet basis functions, handling edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes, establishing significance levels and confidence intervals. Smoothing in time or scale is shown to increase the confidence of wavelet spectra, with empirical formulas provided for the effect of smoothing on significance levels and confidence intervals. The chapter also covers extensions such as filtering, the power Hovmöller, cross-wavelet spectra, and coherence. These statistical significance tests are used to quantitatively measure changes in ENSO variance on interdecadal timescales, revealing significant variations in power during specific periods and a possible 15-yr modulation of variance. The use of new datasets extending back to 1871 allows for a more robust classification of interdecadal changes in ENSO variance.This chapter provides a practical guide to wavelet analysis, focusing on time series analysis of the El Niño–Southern Oscillation (ENSO). It includes a comparison with the windowed Fourier transform, selection of appropriate wavelet basis functions, handling edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes, establishing significance levels and confidence intervals. Smoothing in time or scale is shown to increase the confidence of wavelet spectra, with empirical formulas provided for the effect of smoothing on significance levels and confidence intervals. The chapter also covers extensions such as filtering, the power Hovmöller, cross-wavelet spectra, and coherence. These statistical significance tests are used to quantitatively measure changes in ENSO variance on interdecadal timescales, revealing significant variations in power during specific periods and a possible 15-yr modulation of variance. The use of new datasets extending back to 1871 allows for a more robust classification of interdecadal changes in ENSO variance.