There are three schools of thought concerning this:
One is that modern history is from 1950 onward.
Another is that modern history is from 1899 onward
The final one is that modern history doesn't exist as something
that is modern cannot exist in the past.
Modern history is the considered the time after the "middle
ages", beginning around 1500. Modern history is comprised of two
eras, early modern through about 1800 and late modern which is
followed by contemporary history. Most of this terminology is in
reference to European and American history and their relationship
with other continents.
Modern History is only part of history. Modern history is from
1850 onward in some ways.