The Companion cognitive architecture is aimed at reaching human-level AI by creating software social organisms, systems that interact with people using natural modalities, working and learning over extended periods of time as collaborators rather than tools. Our two central hypotheses about how to achieve this are (1) analogical reasoning and learning are central to cognition, and (2) qualitative representations provide a level of description that facilitates reasoning, learning, and communication. This paper discusses the evidence we have gathered supporting these hypotheses from our experiments with the Companion architecture. Although we are far from our ultimate goals, these experiments provide strong breadth for the utility of analogy and QR across a range of tasks. We also discuss three lessons learned and highlight three important open problems for cognitive systems research more broadly.