Internet education in mathematics is developing as a new mode of teaching with its own characteristics and possibilities, different from the traditional way of teaching. In a study presented in two parts, we attempt to capture the world of Internet teaching of undergraduate mathematics. In the first part of the study (Engelbrecht, J. and Harding, A.: 2004, "Teaching undergraduate mathematics on the web 1: Technologies and taxonomy"), we attempt to create some order in the huge number of activities that are available on the web with a graphical classification of the different types of web courses and discuss some of the technologies involved. In this, the second part of the study, we discuss attributes and implications of this mode of teaching/learning mathematics, also mentioning some of the benefits and concerns. Speculation about the future in such a fluid environment is both risky and fascinating but we nevertheless envisage some possible future trends. Research on this mode of teaching is sparse and open research questions are plentiful. We list possible research issues.