It has been widely acknowledged that future networks need to provide significantly more capacity than nowadays' ones in order to deal with the increasing traffic demands of the users. Particularly in regions where optical fiber are unlikely to be deployed due to economical constraints, this is a huge challenge. One option to address this issue is to complement existing narrow-band terrestrial networks with additional satellite connections. Satellites cover huge areas and recent developments have considerably increased the available capacity, while the cost are decreasing. However, geostationary satellite links have significantly different link characteristics than most terrestrial links, mainly due to the higher signal propagation time, which often renders them not suitable for delay intolerant traffic. This article surveys the current state-of-the-art of satellite and terrestrial network convergence. We mainly focus on scenarios in which satellite networks complement existing terrestrial infrastructures, i.e. parallel satellite and terrestrial links exist, in order to provide high bandwidth connections while ideally achieving a similar end user Quality-of-Experience as in high bandwidth terrestrial networks. Thus, we identify the technical challenges associated with the convergence of satellite and terrestrial networks and analyze the related work. Based on this, we identify four key functional building blocks, which are essential to distribute traffic optimally between the terrestrial and the satellite networks. These are the Traffic Requirement Identification function, the Link Characteristics Identification function as well as the Traffic Engineering function and the Execution function. Afterwards, we survey current network architectures with respect to these key functional building blocks and perform a gap analysis, which shows that all analyzed network architectures require adaptations to effectively support converged satellite and terrestrial networks. Hence, we conclude by formulating several open research questions with respect to satellite and terrestrial network convergence.