Trends often play a dominant role in many empirical time series data, but do we truly understand these trends? What challenges arise when dealing with complex, nonstationary trending time series? How do we model such trends in fields like economics, finance, and climate change? This book provides an overview of recently developed models for trending time series and introduces new nonlinear, nonparametric, and semiparametric methods. Specifically, it offers practical approaches to address the problem of endogeneity in linear trending regression models where the trend component is either weak or strong. Additionally, it proposes a testing procedure for identifying common trends across multiple time series and includes illustrative examples from economics, finance, and climate change. As a practical toolbox, this book equips analysts with essential methods for investigating trends in their research and applications.