The recent emergence of AI-driven code generation models can potentially transform programming education. To pinpoint the current state of research on using AI code generators to support learning and teaching programming, we conducted a systematic literature review with 21 papers published since 2018. The review presents the teaching and learning practices in programming education that utilize these models, the characteristics and performance indicators of the code generation models, and aspects to be considered when utilizing the models in programming education, including the risks and challenges of using code generation models for educational practices. AI code generators can be an assistive tool for both learners and instructors if the risks are mitigated.