The low-altitude economy (LAE) is a new economic paradigm that leverages low-altitude vehicles (LAVs) to perform diverse missions across diverse areas. To support the operations of LAE, it is essential to establish LAE networks that enable LAV management and communications.Existing studies mainly reuse terrestrial networks to construct LAE networks. However, the limited coverage of terrestrial networks poses challenges for serving LAVs in remote areas. Besides, efficient LAV operations also require support such as localization and navigation, which terrestrial networks designed for communications cannot fully provide. Due to ubiquitous coverage and diverse functions, satellites are a promising technology to support LAVs. Therefore, this article investigates satellite-assisted LAE networking. First, we introduce an overview of LAE and satellites, discussing their features, applications, and architectures. Next, we investigate opportunities for satellites to assist LAE from aspects of communication, control, and computation. As all assistance depends on reliable satellite-LAV communications, we propose a satellite-assisted LAE framework to tackle issues caused by the severe path loss and high dynamics in satellite-assisted LAE networks.The case study demonstrates that the distributed MIMO architecture efficiently reduces the required transmission power and extends service duration, while the two-timescale optimization scheme balances the performance and control signaling overheads. Specifically, the proposed framework comprises distributed satellite MIMO, distributed LAV MIMO, and a two-timescale optimization scheme.