Modern electronic textiles are moving towards flexible wearable textiles, so-called e-textiles that have micro-electronic elements embedded onto the textile fabric that can be used for varied classes of functionalities. There are different methods of integrating rigid microelectronic components into/onto textiles for the development of smart textiles, which include, but are not limited to, physical, mechanical and chemical approaches. The integration systems must satisfy being flexible, lightweight, stretchable and washable to offer a superior usability, comfortability and non-intrusiveness. Furthermore, the resulting wearable garment needs to be breathable. In this review work, three levels of integration of the microelectronics into/onto the textile structures are discussed, the textile-adapted, the textile-integrated, and the textile-based integration. The textile-integrated and the textile- adapted e-textiles have failed to efficiently meet being flexible and washable. To overcome the above problems, researchers studied the integration of microelectronics into/onto textile at fiber or yarn level applying various mechanisms. Hence, a new method of integration, textile-based, has risen to the challenge due to the flexibility and washability advantages of the ultimate product. In general, the aim of this review is to provide a complete overview of the different interconnection methods of electronic components into/onto textile substrate.