Th thirties, if your idea of modern ins the same as mine. Percussionists had long performed multiple parts as practical but the modern bass drum pedal and high hat (the cymbals that open and close) are twentieth century inventions. (Aughts and twenties, respectively). Look to jazz for examples. Beyond those two elements, it's difficult to make firm statements about the evolution of the drum kit as they're individual; there are eight basic elements (bass drum, snare, high pitched tom, low pitched tom, high hat, "crash" cymbal, "ride" cymbal, throne) but some drummers forego and/or alter even them, as they're as much or more musical elements as they are instruments (note the cymbals names).