Adaptive control is a very appealing technology, at least in principle. Yet its use has been conditioned by an attitude of distrustfulness on the part of some practitioners. In this paper, we explain why such distrustfulness is warranted, by reviewing a number of adaptive control approaches which have proved deficient for some reason that has not been immediately apparent. The explanation of the deficiencies, which normally were reflected in unexpected instabilities, is our main concern. Such explanations, coupled with remedies for avoiding the deficiencies, are necessary to engender confidence in the technology. These include the unpredictable failure of the MIT rule; the bursting phenomenon, and how to prevent it; the Rohrs' counterexample, which attempted to disqualify all adaptive control algorithms; the notion that identification of a plant is only valid conceptually for a restricted range of controllers (with the implication that in adaptive control, certain controller changes suggested by adaptive control algorithms may introduce instability); and the concept of multiple model adaptive control. 1. Introduction. Adaptive controllers are a fact of life, and have been for some decades. However, theory and practice have not always tracked one another. In this paper, we examine several instances of such a mismatch. These are: • The MIT rule, an intuitively based gradient descent algorithm that gave unpredictable performance; satisfactory explanation of performance started to become possible in the 1980s. • Bursting, a phenomenon of temporary instability in adaptive control algo- rithm implementation of a type observed in the 1970s; explanation and our understanding of avoidance mechanisms only became possible in the 1980s. • The Rohrs' counterexample, which argued that adaptive control laws existing at the time could not be used with confidence in practical designs, because unmodeled dynamics in the plant could be excited and yield an unstable control system. • Iterative controller re-design and identification, an intuitively appealing ap- proach to updating controllers that came to prominence in the 1980s and 1990s, and which can lead to unstable performance. Explanation and an understanding of an avoidance mechanism came around 2000. • Multiple model adaptive control, another intuitively appealing approach to adaptive control with the potential to include non-linear systems. It too can lead to unstable performance; early theoretical development left untouched important issues of the number of controllers to be used, and their location