New edge does not split face I subdivided a face. I then connected the newly added vertex to an existing vertex by selecting both vertices and pressing F
The now newly created edge crosses an existing face, but the face is not partitioned by the new edge (as can be seen in the screenshot below). So, I obviously did something wrong.

So, my question is: how do I split the existing face in two right where the edge is?
P.S.
I'm reaaly new to blender so I don't know the correct terminology to search for; I hope this question is not answered here already.
By selecting the vertices and pressing F you are simply creating a new edge. The faces connected to the vertices are not changed, this behaviour correct.

In this position, delete the problematic face.Select all the vertices and/or edges, which need to be fill and press 
F to fill them with new faces.

Alternatively, before creating the edge which intersects the face, press K to cut the face with the Knife Tool. The knife tool can snap to the vertices along the faces' edge.