Carbon emission is a dynamic process influenced by various factors and accurately forecasting these emissions is conducive in developing reduction strategies. Traditional forecasting methods often fall short of actual situations due to the dynamic, nonlinear, and social characteristic of carbon emissions. The artificial neural network model, capable of capturing the nonlinear patterns in time-series data, is widely used to predict changes in carbon emissions at national, regional, and industrial levels. Among them, BP (Back Propagation) neural network model and the LSTM (Long Short-Term Memory) neural network model are particularly favored by researchers for carbon emission forecast. The prediction accuracy of these models can be enhanced by systematically categorizing the types of factors influencing carbon emissions, enhancing the accuracy of input data, and developing appropriate models that couple linear and nonlinear components. The research reviews the application of artificial neural network models in carbon emission forecast, offering guidance for the future development of carbon emission forecast technologies.