Blenderole

Now it begins to get confused. There’s no way to move freely the pivont point (the pink dot) of an object, with a gizmo for example. You have to position first the 3d cursor to your liking then center the pivot to the 3d cursor. PLUS, sometimes the pivot is called “object’s origin”.

Extremely essential to this, thus, is snapping. Done through SHIFT+S. Options are clearly self-explanatory, but you have to understand what you are moving (Cursor to Selection means moving the 3d cursor to what you have currently selected, a vertex for example). After you’ve placed the cursor where you want the object’s origin to be, you use one of the following buttons:

Fortunately, you don’t have to go through all this when you want to just rotate/scale an object with a different pivot. On the pivot mode options, bellow, you can quickly change which pivot point to use:

References used for this post are:

Blender Underground post by penix1 with an in-depth explanation of Blender Objects Origin
2min video tutorial from Josh (3DMacDaddy)

All this is usefull if you are going to use Mirror, because it mirrors on the object’s origin point.

And if you want to rotate the pivot, you actually have to use a script named Object/Scripts/Axis Orientation Copy.