Trust and trustworthiness are central concepts in contemporary discussions about the ethics of and qualities associated with artificial intelligence (AI) and the relationships between people, organisations and AI. In this article we develop an interdisciplinary approach, using socio-technical software engineering and design anthropological approaches, to investigate how trust and trustworthiness concepts are articulated and performed by AI software practitioners. We examine how trust and trustworthiness are defined in relation to AI across these disciplines, and investigate how AI, trust and trustworthiness are conceptualised and experienced through an ethnographic study of the work practices of nine practitioners in the software industry. We present key implications of our findings for the generation of trust and trustworthiness and for the training and education of future software practitioners.