A swarf handling apparatus installed in a machining tool that performs machining operation accompanied with production of stringy swarf includes a swarf catching device. The swarf catching device includes a holder unit that holds the stringy swarf when the stringy swarf makes contact with the holder unit. The swarf catching device causes the holder unit to be floated in a region around a machining point in such a manner that the position of the holder unit is varied relative to the machining point, for catching the stringy swarf in the holder unit.