The vigorous response of multiwalled carbon nanotubes (MWNTs) to microwave irradiation, leading to the release of a large amount of heat, is used to locally melt a plastic matrix adjacent to the nanotubes within a period of seconds. This results in the intercalation of the MWNTs into the polymer matrix at room temperature without any physical damage to the polymer. The so-called "microwave welding" approach creates a new paradigm for the formation of very strong MWNT-polymer bonds without the use of any adhesive, and represents a significant step forward for the fabrication of functional nanotube composites. Here, we demonstrate the implications of the anisotropic alignment of MWNTs in polymers, patterned conductors/resistors for soft electronics, and high-strength composites, where the MWNTs are 'soldered' to flexible polymer substrates.