Most, if not all, physics undergraduate degree programs include instructional lab experiences. Physics lab instructors, both faculty and staff, are instrumental to student learning in instructional physics labs. However, the faculty-staff dichotomy belies the complex, varied, and multifaceted landscape of positions that lab instructors hold in the fabrics of physics departments. Here we present the results of a mixed-methods study of the people who teach instructional labs and their professional contexts. Recruiting physics lab instructors across the United States, we collected 84 survey responses and conducted 12 in-depth interviews about their job characteristics, professional identities, resources, and experiences. Our investigation reveals that lab instructors vary in terms of their official titles, job descriptions, formal duties, personal agency, and access to resources. We also identified common themes around the value of instructional labs, mismatched job descriptions, and a broad set of necessary skills and expertise. Our results suggest that instructors often occupy overlapping roles that fall in between more canonical jobs in physics departments. By understanding the professional contexts of physics lab instructors, the rest of the physics community can better promote and engage with their critical work, improving laboratory learning both for students and for the lab instructors who teach and support them.