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For Blender 2.8+ Copy and Paste is honoured as standard but selectively, in other words the functions are not available to all editors or contexts as some have their own ‘copy’ functions relative to the type of data being cloned and the editor/operator used to perform the action.

General Copy/Paste

Generally speaking to use copy and paste simply make a selection, a single object or multi-selection group, and press Ctrl + C to Copy, then Ctrl + V to Paste. This clones the selection much the same way as Duplicate Objects (Shift + D) so the new items will appear linked to and moving with the mouse. Press Esc or right-click to reset back to their originating position (same location as the original items) to then edit as normal.

Design note: copy/paste is functionally similar to Duplicate Objects so copying a linked object always produces an unlinked copy – the result will typically incorporate certain instanced properties associated with the originating object e.g. materials, whilst others will be unique e.g. the User ID (Single User or Fake User) and mesh itself.

Copy/Paste behave similar to Duplicate Objects.
The preferred way to clone selections is to duplicate but copy/paste is honoured although not available to all editors, modes or contexts – shown above a simple mesh is copied whilst in Object Mode using the Object menu option. Once done the status bar displays a confirmation message “Copied 1 selected object(s)”.

Copy/Paste & Context

As briefly mentioned above copy/paste is context sensitive, its available subject to the editor and active ‘mode’. For example in Object Mode (3D View) once a selection is made both ‘duplication’ and ‘copy’ are available (Object » Duplicate Objects/Linked and Object » Copy/Paste Objects) whereas for Edit Mode only duplicate is shown (Mesh » Duplicate) allowing for specific element cloning – vertex, edge and/or face. Similarly in Pose Mode copy is available (Pose » Copy/Past Pose) but not duplicate. In the Action Editor frame markers, the data object generally manipulated in this editor, can be copied using Copy Keyframes/Paste Keyframes or Duplicate (Key » Copy/Paste Keyframes or Key » Duplicate).

Design note: in each instance where copy/paste is available, Ctrl + C and Ctrl + V shortcuts remain the same regardless of the label shown in the respective menu.

Copy/Paste availability differs depending on context
The availability of Copy/Paste and Duplicate depends on the editor and context, in the Action Editor for example Keyframe markers can be edited and managed a number of ways due to the data they contain whereas the pose itself in Pose Mode can only be copied and pasted.

Copy/Paste vs Duplication

Generally speaking although copy and paste functions like Duplicate Objects it has one or two advantages based on the context within which its used, duplication for example creates an immediate clone of a selection that appears in place, that is meshes, keyframe markers etc. all appear co-located with originating object. Copy/paste however, can be used to copy selections from one location to another, a keyframe marked in the Action Editor for example copied from one frame to another indicated by the timeline slider. Duplicate does not do this it clones a selection in place (albeit initially responsive to mouse movement).

Copy/Paste between frames
Using copy/paste to clone a keyframe (from frame 1) into another position marked by the timeline slider (at from 140), duplicate does not accommodate this action.

Copy/Paste & Collections

Copy/paste can also be used to clone content between Collections in the Outliner. Here, similar to using copy/paste in the Action Editor and others, copy will clone the highlighted data from one Collection group and paste it into another (once similarly highlighted). As with Duplicate Objects this creates a unique item (Single User/Mesh ID) that may then include some instanced properties from the originating object, i.e. Materials.

Design note: for more on Collections see here.

Copy/Paste between Collections
Copy/paste can be used to clone content between Collections in the Outliner, simply select the object(s) to be copied then the Collection into which the new objects are to appear, and paste in place.

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