Forecasting serves as a critical cornerstone for strategic planning, operational efficiency, and risk mitigation across modern civilization. By converting historical data into actionable forward-looking insights, it enables organizations and governments to anticipate market shifts, optimize resource distribution, and safeguard against systemic uncertainties. Predictive modeling is a fundamental task in many fields, such as finance, economics, engineering, and artificial intelligence. The aim of this paper is to summarize the methods of statistics and machine learning, outline their inherent challenges, and project future research directions. This paper mainly discusses traditional statistical methods (including Autoregressive Integrated Moving Average [ARIMA] and regression analysis), machine learning approaches (such as Random Forest and Support Vector Machines [SVM]), and deep learning models (such as Long Short-Term Memory [LSTM] networks and hybrid time series-ML models). Nowadays, as these interconnected fields become increasingly complicated, practitioners face severe challenges regarding data quality, computational complexity, and mathematical interpretability. This paper comprehensively reviews these methodologies, establishes a comparative taxonomy, and delineates the evolutionary trajectory of future forecasting applications.