Abstract: Artificial neural networks are mathematical models that emulate biological neural systems. They have been used in classification, pattern recognition, and time-series analysis. In time-series analysis, neural networks can be used for forecasting but also to determine how many and which past values are required to predict the future. Determination of this 'lag space' sheds light on the nature of the dynamics and permits development of minimal models capable of replicating the dynamics. I will highlight applications of neural networks in the real world as models that classify, forecast, and analyze data while emphasizing their use in determining the lag space.