This paper studies Time Series Extrinsic Regression (TSER): a regression task of which the aim is to learn the relationship between a time series and a continuous scalar variable; a task closely related to time series classification (TSC), which aims to learn the relationship between a time series and a categorical class label. This task generalizes time series forecasting (TSF), relaxing the requirement that the value predicted be a future value of the input series or primarily depend on more recent values. In this paper, we motivate and study this task, and benchmark existing solutions and adaptations of TSC algorithms on a novel archive of 19 TSER datasets which we have assembled. Our results show that the state-of-the-art TSC algorithm Rocket, when adapted for regression, achieves the highest overall accuracy compared to adaptations of other TSC algorithms and state-of-the-art machine learning (ML) algorithms such as XGBoost, Random Forest and Support Vector Regression. More importantly, we show that much research is needed in this field to improve the accuracy of ML models. We also find evidence that further research has excellent prospects of improving upon these straightforward baselines.