Generative artificial intelligence (GenAI) has opened new possibilities for designing learning analytics (LA) tools, gaining new insights about student learning processes and their environment, and supporting teachers in assessing and monitoring students. This systematic literature review maps the empirical research of 41 papers utilizing GenAI and LA and interprets the results through the lens of the LA/EDM process cycle. Currently, GenAI is mostly implemented to automate discourse coding, scoring, or classification tasks. Few papers used GenAI to generate data or to summarize text. Classroom integrations of GenAI and LA mostly explore facilitating human-GenAI collaboration, rather than implementing automated feedback generation or GenAI-powered learning analytics dashboards. Most papers use Generative Adversarial Network models to generate synthetic data, BERT models for classification or prediction tasks, BERT or GPT models for discourse coding, and GPT models for tool integration. Although most studies evaluate the GenAI output, we found examples of using GenAI without the output validation, especially when its output feeds into an LA pipeline aiming to, for example, develop a dashboard. This review offers a comprehensive overview of the field to aid LA researchers in the design of research studies and a contribution to establishing best practices to integrate GenAI and LA.