A drain cleaning apparatus includes a handle and a clog-catching member detachably connected to the handle. Wings, barbs or hooks project radially from the clog-catching member. The wings, barbs or hooks provide an angled projection that catches and holds a clump of debris in a drain pipe for pulling the clump out and unclogging the drain. Different end tools can be removably connected to a clog-catching member or to a smooth extension member to provide multifunctionality. The handle, clog-catching members, smooth extension members and tools can be connected together using a quick-connect connector, such as a snap fastener, a keyhole fastener or a side-release buckle, or a threaded connector. In addition to drain cleaning, the apparatus can be fitted with tools such as a magnet, grabber, light, camera and/or video for retrieval of objects and inspection of a space that is difficult to view directly.