Ultrathin films of single-walled carbon nanotubes (SWNTs) represent an attractive, emerging class of material, with properties that can approach the exceptional electrical, mechanical, and optical characteristics of individual SWNTs, in a format that, unlike isolated tubes, is readily suitable for scalable integration into devices. These features suggest the potential for realistic applications as conducting or semiconducting layers in diverse types of electronic, optoelectronic and sensor systems. This article reviews recent advances in assembly techniques for forming such films, modeling and experimental work that reveals their collective properties, and engineering aspects of implementation in sensors and in electronic devices and circuits with various levels of complexity. A concluding discussion provides some perspectives on possibilities for future work in fundamental and applied aspects.