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For example, I have two different objects. One cube and another- sphere. Can I somehow make cube change its shape identical to the sphere through animation? I mean I can do it manually with shape keys but is there some way to do it procedurally by just having start and final shapes even with different amount of vertices? The thing is I have two much more complex objects and transforming one into another is a hell of an ordeal.

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    $\begingroup$ Procedural way with shape keys for 2 objects is Join As Shapes option in the Shape Key panel (object must have the same vertex count). Cast modifier could be a way for transforming 1 object (although likely not any shape as complex ones can become a mess). One more way is with Keyed particles but that will mean breaking objects into particles obviously. It all depends on what transition are you going to with and how complex objects are. $\endgroup$ – Mr Zak Jun 6 '17 at 11:48
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Morphing objects with different vertex count is impossible AFAIK with the blender tools, unless you use a scripting. Here's a temporary solution though. It uses a to sphere tool. enter image description here

I have three objects here with a different vertex count. I'll use a sphere as a midpoint for all transformations.
enter image description here

Add a shape key (Key 1) and set its value to 1.000. Enter Edit Mode and use To Sphere tool (Shift+Alt+S,1). Then hit Ctrl+V-->Smooth Vertex. Hold Shift+R to repeat it (set smoothing value to 1.000 in a Tool Shelf) unless the vertices are relaxed. Then repeat the to sphere operation. enter image description here

Do the same with the other objects (every one should transform to the sphere of an equal size). Finally keyframe the shape keys values and visibility of the objects on a timeline. enter image description here

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