We describe a general approach to dynamic sparsity modelling in time series and state-space models. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing dynamic variable　inclusion/selection. We discuss Bayesian model estimation and prediction in dynamic regressions, time-varying vector autoregressions and multivariate volatility models using latent thresholding. Substantive examples in macroeconomics and financial time series show the utility of this approach to dynamic parameter reduction and time-varying sparsity modelling in terms of statistical and economic interpretations as well as improved predictions.