Most concepts serve temporary and partial purposes in an activity system. We might call them action-level concepts. But there are also concepts that become durable orientation bases for the entire activity, or even for coalitions of multiple activity systems. We might call those activity-level concepts. Cultural-historical activity theory offers a set of foundational ideas for the study and practical fostering of concept formation in the wild, particularly in the current phase of the fourth generation of activity theory. The emerging fourth generation of activity theory zooms on heterogenous activity coalitions aimed at resolving wicked societal problems, or runaway objects, and creating sustainable and equitable alternatives to capitalism. The foundational ideas may be condensed in two principles, namely the principle of double stimulation and the principle of ascending from the abstract to the concrete. The principle of double stimulation incorporates volition and agency as integral aspects into our understanding of concept formation in the wild. The principle of ascending from the abstract to the concrete leads to the distinction between empirical and theoretical concepts, to the idea of a germ cell as the starting point and core of a theoretical concept, and to the theory of expansive learning.