The recent emergence of LLM-based code generation models can potentially transform programming education. To pinpoint the current state of research on using LLM-based code generators to support the teaching and learning of programming, we conducted a systematic literature review of 21 papers published since 2018. The review focuses on (1) the teaching and learning practices in programming education that utilized LLM-based code generation models, (2) characteristics and (3) performance indicators of the models, and (4) aspects to consider when utilizing the models in programming education, including the risks and challenges. We found that the most commonly reported uses of LLM-based code generation models for teachers are generating assignments and evaluating student work, while for students, the models function as virtual tutors. We identified that the models exhibit accuracy limitations; generated content often contains minor errors that are manageable by instructors but pose risks for novice learners. Moreover, risks such as academic misconduct and over-reliance on the models are critical when considering integrating these models into education. Overall, LLM-based code generation models can be an assistive tool for both learners and instructors if the risks are mitigated.