Peer Instruction gives practice in the abstract language of physics, addresses common misconceptions among students, and is more effective than traditional lecturing. However, it is not clear what makes Peer Instruction effective nor how we might improve the method. An emerging perspective is that what makes Peer Instruction effective is how it stimulates certain cognitive processes. Research also indicates that providing rules for discussion may improve the effect of peer instruction. Hence, we wanted to answer two research questions in this study: (i) What cognitive learning processes occur during peer discussions? (ii) How do students follow discussion rules? To answer our research questions, we recorded and thematically analyzed peer discussions during Peer Instruction in an introductory physics course. The most prevalent cognitive process during peer discussions was decoding the problem. The most prevalent type of explanation was explanations with physics concepts, which usually led the students to an incorrect answer. The next most prevalent type of explanation was explanation with physics models, which usually led the students to the correct answer. The students also explained with reference to their experience or examples—intuitive or analogical explanations—and it usually added little to the conversation, was wrong, or created confusion. Some discussion rules had limited impact, prompting suggestions for rule improvements to optimize Peer Instruction. Our work contributes to the literature on Peer Instruction with a cognitively based description of the learning processes and how we might further improve and ensure the effectiveness of Peer Instruction. Published by the American Physical Society 2024