In recent years, multifractal detrended fluctuation analysis (MF-DFA) has become an important tool for detecting the scale and long correlation of non-stationary time series. With the continuous development of multifractal theory, researchers have widely applied it in physics, chemistry, biology, economy, etc. In this paper, we briefly review various applications of MF-DFA, and present some empirical research using one- and two-dimensional (2D) MF-DFA. 1D MF-DFA is always applied in financial markets, energy markets, heartbeat, and atmospheric science. Furthermore, 2D MF-DFA has been studied in surface science such as image segmentation, medical image classification. In this paper, we use 1D MF-DFA to explore the market efficiency of Korean stock market, and adopt 2D MF-DFA to segment images such as the license plate and hepatic cell image. In addition, we apply the proposed algorithm to segment transmission lines under icing condition, and the proposed method achieves satisfactory segmentation results.