How does Mendeleev's Periodic Table relate to the modern one?

One could argue that our current periodic table began with Mendeleev's.  Although the information found on today's table (like average atomic radius, electronegativity, etc.) is outside of Mendeleev's scope, designing the table on repeated patterns that become apparent when you arrange the elements in order of increasing atomic mass is exactly how we do it today (well, increasing atomic number).  Mendeleev's table is a classic example of how the scientific process can work beautifully.  He predicted not only the presence of yet-to-be discovered elements, but did a fairly decent job of predicting what characteristics they should have.

The neat part is that there are elegant patterns (in things like atomic radius, reactivity, types of ions formed, etc.) that can be seen in today's table that Mendeleev would have had no inkling about.

To be clear though, the feature that connects Mendeleev's table to today's is arranging the elements in increasing order of mass (Mendeleev's) or ultimately atomic number (today).