The various models for $(\infty, 1)$-categories each lead to a number of approaches to higher $(\infty, n)$-categories. In this talk we'll consider some of the generalizations of Segal categories and complete Segal spaces, as well as known and conjectured comparisons between them.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/6477