Rotating on X and Z axis only

The simplest thing would be if your two objects are on the same plane.

Barring that, you can at least pretend they are by zeroing out the depth axis before calculating your goal rotation:

 var displacement = player.position - transform.position;
 displacement.z = player.position.z; //pretend objects are at same height
 var rotation = Quaternion.LookRotation(displacement); //ed: thanks to Bunny83

By some clever vector multiplication, you could even make that axis-agnostic, but that's probably better left for another day.

If you need more control than that, I suppose you could try something like this:

• Get a rotation from Slerp()

• Convert that rotation to its vector form using its `eulerAngles` property

• Zero out one or more axes

• Convert that back into a rotation using `Quaternion.Euler()`

Also remembers that if you're using rigidbodies, you can set rotation and position constraints locking them on a particular axis, which is sometimes very handy for 2D simulation.