With the Default Cube.
Just as a cube turns into a sphere with enough levels of Catmul Clarke Subdivision surface, can make it a tear drop.
Add the cube, in edit mode select top face and scale to 0. S0. making the top face a zero area, (edge length 0) ... all 4 verts in same location quad face. Without quad faces, sub'd modifier results look like rubbish.
Assign the cube a subdivision modifier. To fatten the teardrop, scale the bottom face in edit mode... to elongate move bottom face down, etc.
For example sake have added a shapekey to the sub'd cube and scaled its top face to zero. Here I scrub the influence to go from sphere to tear, scale the bottom face to make it fatter, or move it around
Scaling the top face of cube to zero, (a pyramid) is akin to a 4 sided cone. Add Mesh Cone, To make sure it has a top face, give it a nominally small minor radius.
Add sub'd modifier will produce result similar to above.
The major difference being the rotation of 45 degrees about Z. Compare the front views of above and below.
Example of 3 subdiv levels on cone, scaled in X, Y and Z. Showing front top and right view. 2 of the base cones corner verts are higlighted in red, (connected to 3 edges not 4)
Looking at animation above, could not help but notice it looks very similar to using a lattice modifier to deform a mesh. hence, have added this as a quick addition, so many ways to skin a cat in blender.
Add a new lattice to scene and transform and scale, in object mode, such that the lattice nicely encompasses the sphere object. (pretty much so it matches models bounding box).
A lattice modifier is added to the sphere object pointing to the newly created lattice. Now in edit mode of the lattice select the top four points and scale to zero.
Example of deforming a lattice (as shape) to deform the sphere, once again I've used a sub'd cube for example sake, try it with Suzanne (the monkey). By way of example have given this lattice a bit more resolution (grid) than the default, and used proportional editing, when transforming top 4 points
Same lattice as above, deforming a 3-Icosphere