This paper starts with a survey of some recent results on least-squares (LS) and LS-based self-tuning regulators (STR). Several long-standing problems concerning the basic properties of LS-based STR, such as stability, optimality, consistency and the best convergence rate, are solved within a unified framework. Some previously related results are also subsumed and extended. Various new techniques for analysing LS-based adaptive tracking systems are presented, which may also be useful for analysing other adaptive control problems.