Most existing works on multi-task learning (MTL) assume the same input space for different tasks. In this paper, we address a general setting where different tasks have heterogeneous input spaces. This setting has a lot of potential applications, yet it poses new algorithmic challenges - how can we link seemingly uncorrelated tasks to mutually boost their learning performance? Our key observation is that in many real applications, there might exist some correspondence among the inputs of different tasks, which is referred to as pivots. For such applications, we first propose a learning scheme for multiple tasks and analyze its generalization performance. Then we focus on the problems where only a limited number of the pivots are available, and propose a general framework to leverage the pivot information. The idea is to map the heterogeneous input spaces to a common space, and construct a single prediction model in this space for all the tasks. We further propose an effective optimization algorithm to find both the mappings and the prediction model. Experimental results demonstrate its effectiveness, especially with very limited number of pivots.