Deep learning has emerged as an effective solution for time series forecasting due to its superior ability to capture complex relationships and patterns within temporal data. A typical approach involves learning these tasks individually and training a separate neural network for each task， which has yielded fruitful results in time series forecasting. Recent advances in multitask learning techniques have demonstrated their advantages in terms of performance， computation， and memory usage by jointly processing multiple prediction tasks through learning shared knowledge. This paper presents the first comprehensive review of methods for multitask time series forecasting. It begins by summarizing deep models for time series forecasting， represented by convolutional neural networks， recurrent neural networks， attention mechanisms， Transformer and graph neural networks， including datasets， model characteristics， and performance. Subsequently， an in-depth analysis of deep multitask time series forecasting models is conducted， categorizing them based on parameter sharing methods and the location of parameter sharing （or interaction）， and discussing some common multitask time series forecasting frameworks. Finally， this paper summarizes the challenges faced by deep time series forecasting and offers insights into future research trends.