Why are rigid bodies not interacting? First of all, here's the blend file: 



I'm trying to recreate the "flip table" animation: I have two rigid bodies (three counting the floor), a table and a cube.

The table is resting on the floor, it is simply put a flat parallelepiped with four slim as the legs. I've set it as an 'active' object (50kg) and the shape is a 'mesh', since I want to interact with the zone between the legs.

Then there's the cube which it is the one interacting with the table. I want it to hit the border in order to give it a rotation, like somebody actually "flipping" it. It is an 'active animated' object (1kg), with shape 'convex hull'.

I set the cube as being under the edge of the table at t=0, and sometime later I shift it on the z-direction until it surpasses it. I insert both framekeys, start the simulation, and... nothing.

The two objects don't interact. The cube passes through the table and each goes its own way.

Does anybody have any idea about what's happening? What do I have to do in order for the two objects to interact? I will post further details if needed, on the file there is my simulation btw.

Bonus question: I tried to raise the table and rotate it to see how it would fall on the floor... and it kinda bounces off. What's causing it? How can I make it behave like a real heavy table? 

For the rotated table, here's the blend:
I downloaded your file and tested couple things, and the problem seems to be the table having weird scale (5.483, 5.483, 0.369). By applying the scale (In object mode, select the table, hit Ctrl+A and select Scale) the physics start to work as expected in both files.  

I also noticed your some other issues with your table which might cause problems later (the board has at four meshes overlapping and the legs have inverted normals), but those are not in scope of this question.