(Not a historian but a social science/civics teacher) That completely depends on your definition. Often we use the word modern to mean current, or contemporary. What the scope of that is, is completely up to the user of the phrase. Usually it's marked by some important event or development. But that's probably not what you're looking for.

There is a time period that is known as the modern era, the age of modernism or modernity. This ranges from the second half of the 19th up to and including the first half of the 20th century (roughly). This period was marked with radical societal changes in politics (e.g. the rise of democracy, liberalism and socialism), technology and science (e.g. the industrial revolution, the development of social sciences) and culture (e.g. the rise of more abstract artforms such as impressionism).