The concept of special radicals, exemplified by the prime, nil, Jacobson and Brown-McCoy radicals, was central to Andrunachievici’s seminal papers [1]. Subsequently questions posed in these papers have been answered, new ones have arisen, many answered in turn, and interesting open problems remain. In these papers the result which has become known as Andrunachievici’s Lemma also appeared. In the intervening period versions of this lemma have been proved for various kinds of non-associative rings. We shall give an account of these developments.