This talk will introduce the homotopy coherent cellular nerve of a bicategory, which defines a fully faithful functor from the category of bicategories and normal pseudofunctors to the category of presheaves over Joyal's category Θ_2. We will show that this functor restricts to the right part of a Quillen adjunction between Lack's model structure for bicategories and Ara's model structure for 2-quasi-categories.