Generative artificial intelligence (GenAI) impacts higher education assessment and learning outcomes, which are closely related and intertwined. Literature suggests that educators and researchers have many varied concerns regarding student assessment in the higher education GenAI context, such as how to assess students' learning and the new (refocused) learning outcomes that emerged in GenAI-facilitated learning environments. To provide evidence-based insights into and answers to these concerns, we conducted a scoping review by collating literature in relevant research areas. Following a five-stage scoping review framework, we collaboratively collected and coded 34 studies. The three assessment approaches identified in the review were traditional assessment, innovative and refocused assessment and GenAI-incorporated assessment. The new, refocused learning outcomes identified were career-driven competencies and lifelong learning skills. The review also revealed that most research designs were qualitatively oriented (e.g., with exploratory design, descriptive research, ethnographic research and phenomenological research). This study proposes a holistic diagram showing the current research status and trends. It suggests five future research directions: innovative assessment designs, collaborations among assessment approaches, new learning outcomes, relationships between assessment approaches and learning outcomes, and quantitative or mixed research studies.