Quantile regression is a powerful technique that extends the capability of the traditional least-squares method for regression analysis. This talk gives an overview of some recent advances in quantile regression for spectral analysis of time-series data. In particular, it discusses a new type of periodogram which is constructed from quantile regression with harmonic (trigonometric) regressors. The ordinary periodogram, being the squared modulus of the Fourier transform, is widely used for time series analysis, not only to detect hidden periodicities as originally intended, but also to characterize more complicated time-domain dependence in the frequency domain. Based on a reformulation of the ordinary periodogram in terms of least-squares harmonic regression, the new periodogram, called quantile periodogram, is obtained by replacing the least-squares criterion with the quantile regression criterion. Like quantile regression in general, the quantile periodogram offers a richer view than the one provided by the ordinary periodogram for spectral analysis time-series data. The quantile periodogram at the median (also known as the Laplace periodogram) serves as a robust alternative to the ordinary periodogram, just like the sample median does to the sample mean. The quantile periodogram can be interpreted in terms of level-crossings. Application of the quantile periodogram to sunspot numbers and financial indices reveals some interesting properties of these data that cannot be seen in the ordinary periodogram.