How would you compare the three types of bonds based on what happens to the valence electrons of the atoms?

The modern covalent bond is conceived to be a region of high electron density between 2 positively charged atomic nuclei such that internuclear repulsion (on the basis of the electrostatic repulsion of like charges) is NEGATED, and a net attractive force results. Covalent bonds are thus highly directional, and if we map electron density between the bound nuclei, there is maximum density along the direction of the bond.

I am not entirely happy with this diagram, as it does not reflect the the maximized electron density between the hydrogen atoms.....Here is another attempt:

The point I wish to illustrate is that there is high electron density BETWEEN the nuclei.

On the other hand, #"ionic bonding"# results from the transfer of electrons between a metal (a reducing agent), and a non-metal (an oxidizing agent), such that discrete charged particles, #"ions"#, result, which are held together in an electrostatic lattice. In an ionic structure, which is strongly NON-MOLECULAR, every cation, every positively charged particle, is electrostatically to every other anion, every negatively charged particle in the ionic lattice.

Of course, cations, and anions, are electrostatically repelled by every cation, and anion is the lattice, but if you sum up attractive versus repulsive interactions across the lattice, which can certainly be done quantitatively, a net attractive force operates over the entire lattice. And thus ionic solids have high melting and boiling points, which reflects their molecularity (which is ZERO), and tend to be brittle solids, while having very high melting points. Solutions of ionic solids, when they can be dissolved in a solvent, thus also exhibit electrical conductivity.

And lastly we come to #"metallic bonding"#, which is observed for metals. Here each atom in the metallic lattice contributes one or two (or more) valence electrons to the overall lattice, to leave a structure which is often described as #"positive ions in a sea of electrons"#. Because the electrons are delocalized over the entire lattice, the metal nuclei can move with respect to each other, while still maintaining a chemical bond. Metals thus tend to be #"(i) malleable"#, meaning that they can be beaten out into a sheet, #"(ii) ductile"#, meaning that they can be drawn out into a wire, and (generally) #"(iii) electrically conducting"#. That is they can conduct an electric charge on the basis of the delocalized electrons.

And in this way the properties of metals, covalent solids, molecular gases and liquids can be rationalized on the basis of their peculiar electronic structure.