Trend usually plays a dominant role in many empirical time series data. But do we really understand trends in these time series data? What are the difficulties in dealing with complex trends when we encounter nonstationary trending time series in practice? How do we model the trending behaviors in the empirical data in economics, finance, and climate change? This book offers an overview of recently developed trending time series models and introduces new nonlinear, nonparametric, and semiparametric methods. In particular, it proposes useful methods to solve the problem of endogeneity in the linear trending regression models when the trend component is either weak or strong. The book also proposes a testing procedure for common trends among trending time series and provides some illustrative examples for using these models and methods in economics, finance, and climate change. Serving as a practical toolbox, this book equips empirical analysts with essential tools to investigate trends in their work and research.