Permanent magnet brushless machines having Halbach array exhibit a number of attractive features. Therefore, they have been increasingly applied to different market sectors, including aerospace, industrial, domestic, renewable, and healthcare, etc. The need of fast global optimization, cost-effective design, and physical understanding of the relationship between parameters and performance requires a powerful analytical model. This thesis develops a general analytical model which is capable of predicting the electromagnetic performance of slotted/slotless permanent magnet brushless machines with both even- and odd-segment Halbach array, having different magnet remanence, magnetization angle and arc for each single magnet segment. The validity of proposed analytical model is examined by finite-element analyses. The price of Neodymium Iron Baron magnet has been raised rapidly over the last few years, which has increased the awareness of cost-effective design and leads the magnet usage efficiency, viz. the ratio of average output torque over permanent magnet volume, to be an important design concern for industry applications. Meanwhile, the needs of high electromagnetic performance including lower torque ripple and sinusoidal air-gap flux density are also critically required. In order to meet such demands, the magnet poles having unequal-magnet height, modular high cost and low cost magnets, together with Halbach magnetization are proposed in this thesis. Based on the developed analytical models, extensive investigation has been performed. Furthermore, in order to fast optimize design parameters, e.g. optimal magnet arc ratio for 2-segment Halbach array and split ratio for external rotor PM machine, two analytical models are developed and validated by finite-element analysis and measurements. With the aid of developed analytical models and finite element analyses, the findings provide useful guidelines for design and analysis of permanent magnet brushless machine having conventional and proposed Halbach arrays.