Over the past several decades, a significant amount of research has been performed in the area of high-resolution signal parameter estimation. It is a problem of significance in many signal processing applications including direction-of-arrival estimation in which the locations of multiple sources whose radiation is received by an array of sensors are sought. Much of the research has focussed on approaches based on the formation of optimal weight or copy vectors, procedures derived from the conventional practice of beamforming. This class of approached to parameter estimation problems has come to be known as high-resolution spectral analysis/beamforming since the introduction of the maximum entropy (MEM) method by Burg in 1967, and the maximum-likelihood (ML) method by Capon in 1969. These techniques provide increased resolution and accuracy over their predecessors (including conventional beamforming, but suffer from model mismatch. MUSIC and ESPRIT are recently developed geometric techniques that exploit the underlying model and thereby achieve significant improvements in performance. In this paper, these techniques are summarized. From basic physical principles, it is shown that ESPRIT is actually a multidimensional null steering algorithm, an interpretation with significant intuitive appeal. Finally, optimal signal copy vectors that naturally arise from the algorithm are presented, and their properties as beamforming vectors for this class of problems are discussed.