This background paper was commissioned by ITPNZ to provide information about effective teaching and learning practices for e-learning in tertiary education, that would assist the wider ITPNZ project to enhance learning outcomes for Mäori e-learners. It complements a separate report analysing 2004 Ministry of Education data on tertiary students and their participation in courses using ICT. What we have aimed to do is to distil the main messages coming from recent thinking on effective teaching and learning, and the main messages coming from recent evidence on the use of e-learning in blended tertiary courses. These show consistencies. These messages are presented in the context of the data on e-learning in New Zealand tertiary institutions, and material related to indigenous learning in overseas countries, and Mäori e-learning. There are three useful examples of the latter; but we found very little material related to indigenous elearning overseas. We conclude with an overview of some issues and challenges related to teaching and learning in tertiary environments.