In this article, we draw on previous reports from physics, science education, and women's studies to propose a more nuanced treatment of gender in physics education research (PER). A growing body of PER examines gender differences in participation, performance, and attitudes toward physics. We have three critiques of this work: (i) it does not question whether the achievements of men are the most appropriate standard, (ii) individual experiences and student identities are undervalued, and (iii) the binary model of gender is not questioned. Driven by these critiques, we propose a conception of gender that is more up to date with other fields and discuss gender as performance as an extended example. We also discuss work on the intersection of identities [e.g., gender with race and ethnicity, socioeconomic status, lesbian, gay, bisexual, and transgender (LGBT) status], much of which has been conducted outside of physics. Within PER, some studies examine the intersection of gender and race, and identify the lack of a single identity as a key challenge of "belonging" in physics. Acknowledging this complexity enables us to further critique what we term a binary gender deficit model. This framework, which is implicit in much of the gender-based PER, casts gender as a fixed binary trait and suggests that women are deficient in characteristics necessary to succeed. Alternative models of gender allow a greater range and fluidity of gender identities, and highlight deficiencies in data that exclude women's experiences.We suggest new investigations that diverge from this expanded gender framework in PER. [This paper is part of the Focused Collection on Gender in Physics.]