To provide a lathe having a simply structured product collection device.

The lathe includes a spindle 13 and a back face spindle 17 disposed facing the spindle 13. An impeller 30 is gripped by a chuck 26 provided at the back face spindle 17. A container body 33 is disposed to surround the impeller 30. The impeller 30 is rotated by the back face spindle 17 to generate suction air flow inward the container body 33 from a machining position. A product Wa machined in the machining position is collected into the container body 33 by the suction air flow.