Grothendieck in his 1984 "Esquisse d'un programme" (Section 2) wrote (English translation):

" ..,people still obstinately persist, when calculating with fundamental groups, in fixing a single base point, instead of cleverly choosing a whole packet of points which is invariant under the symmetries of the situation, which thus get lost on the way. In certain situations (such as descent theorems for fundamental groups `a la van Kampen) it is much more elegant, even indispensable for understanding something, to work with fundamental groupoids with respect to a suitable packet of base points,.."

Question: Does anyone have any reference to relevant work on "descent theorems for fundamental groups"?

Relevant to this question is this mathoverflow discussion on several base points.

Grothendieck in his 1984 "Esquisse d'un programme" (Section 2) wrote (English translation):

" ..,people still obstinately persist, when calculating with fundamental groups, in fixing a single base point, instead of cleverly choosing a whole packet of points which is invariant under the symmetries of the situation, which thus get lost on the way. In certain situations (such as descent theorems for fundamental groups `a la van Kampen) it is much more elegant, even indispensable for understanding something, to work with fundamental groupoids with respect to a suitable packet of base points,.."

Question: Does anyone have any reference to relevant work on "descent theorems for fundamental groups"?

Relevant to this question is this mathoverflow discussion on several base points.