Teachers use multiple representations to communicate the concepts of bonding, including Lewis structures, formulas, space-filling models, and 3D manipulatives. As students learn to interpret these multiple representations, they may develop misconceptions that can create problems in further learning of chemistry. Interviews were conducted with 28 high school physical science, high school chemistry, and general chemistry students. The interviews focused on identifying student understanding of, and misconceptions about, covalent and ionic bonding representations through analysis of both student-created and expert-generated representations. Misconceptions about bonding representations were identified regarding four themes: (i) periodic trends, (ii) electrostatic interactions, (iii) the octet rule, and (iv) surface features. The Bonding Representations Inventory (BRI) was developed to quantify the prevalence of these misconceptions. The BRI was administered to 1072 high school chemistry, advanced placement chemistry, and general chemistry students across the United States. Content validity was determined through expert validation of the items, and concurrent validity was established by comparing the three groups of students. Reliability was determined through individual item analysis and through Ferguson's d. Suggestions are offered for using the BRI in high school and general chemistry classrooms to inform the teaching of both bonding and representations.