For a gauge invariant system of quantum fields to be a self-consistent framework for describing various interactions, mechanisms responsible for short-range interactions must be found (Sections 10.1 and 10.2), and its renormalizability be proven (Section 10.3). In addition, nonabelian gauge theories exhibit some novel features, which have suggested certain interpretations concerning the structure of the vacuum state and the conditions for the quantization of physical parameters such as electric charge. Thus, a new question, which had not appeared in the investigations of Abelian-gauge-invariant QED or of other, nongauge-invariant, local field theories, has posed itself with some urgency, and in recent years become a favorite research topic among a sizable portion of mathematics-oriented physicists. This is the question of the global features of nonabelian gauge field theories (Section 10.4). Thus this chapter reviews the formation of the conceptual foundations of gauge theories, both as a theoretical framework and as a research programme, and points to some questions that remain to be addressed by future investigators.