Overcoming the problem of spectrum scarcity will require innovative new ideas in the area of spectrum management for radio networks. DARPA's three-year Spectrum Collaboration Challenge, launched in 2017, gives teams of researchers the opportunity to develop state-of-the-art software-defined radio networks that autonomously collaborate with other networks to maximize the efficiency of spectrum use while delivering real-world traffic loads. In this talk, we describe the background, problem statement, and open research problems of the challenge. Furthermore, we present our prize-winning radio network design, which was developed and implemented by a multi-university team of researchers and placed among the ten best designs of the first phase of the competition.