question: This chapter presents a survey of some recent methods used in economics and finance to account for cyclical dependence and account for their multifaced dynamics: nonlinearities, extreme events, asymmetries, non-stationarity, time-varying moments. To circumvent the caveats of the standard spectral analysis, new tools are now used based on copula spectrum, quantile spectrum and Laplace periodogram in both non-parametric and parametric contexts. The chapter presents a comprehensive overview of both theoretical and empirical issues as well as a computational approach to explain how the methods can be implemented using the R Package.