This paper presents a review of some modern approaches to trend extraction for one-dimensional time series, that is one of the major tasks of time series analysis. The trend of a time series is usually defined as a smooth additive component which contains information about the time series global change and we discuss this and other definitions of the trend. We do not aim to review all the novel approaches, but rather to observe the problem from different viewpoints and from different areas of expertise. The paper contributes to understanding the concept of a trend and the problem of its extraction. We present an overview of advantages and disadvantages of the approaches under consideration, which are: the Model-Based Approach, nonparametric linear filtering, Singular Spectrum Analysis, and wavelets. The Model-Based Approach assumes the specification of a stochastic time series model, which is usually either an ARIMA model or a state space model. The nonparametric filtering methods do not require specification of model and are popular because of their simplicity in application. We discuss the Henderson, LOESS, and Hodrick-Prescott filters and their versions derived by exploiting the Reproducing Kernel Hilbert Space methodology. In addition to these prominent approaches, we consider Singular Spectrum Analysis (SSA) and wavelet methods. Singular Spectrum Analysis is widespread in the geosciences; its algorithm is similar to that of Principal Components Analysis, but SSA is applied to time series. Wavelet methods are the de facto standard for denoising in signal procession and recent works revealed their potential in trend analysis.