Looking from a global perspective, the landscape of online social networks is highly fragmented. A large number of online social networks have appeared, which can provide users with various types of services. Generally, the information available in these online social networks is of diverse categories, which can be represented as heterogeneous social networks (HSN) formally. Meanwhile, in such an age of online social media, users usually participate in multiple online social networks simultaneously to enjoy more social networks services, who can act as bridges connecting different networks together. So multiple HSNs not only represent information in single network, but also fuse information from multiple networks. Formally, the online social networks sharing common users are named as the aligned social networks, and these shared users who act like anchors aligning the networks are called the anchor users. The heterogeneous information generated by users' social activities in the multiple aligned social networks provides social network practitioners and researchers with the opportunities to study individual user's social behaviors across multiple social platforms simultaneously. This paper presents a comprehensive survey about the latest research works on multiple aligned HSNs studies based on the broad learning setting, which covers 5 major research tasks, i.e., network alignment, link prediction, community detection, information diffusion and network embedding respectively.