A method of controlling discard operations is performed in a system that includes a host device and a data storage device. The method includes providing a shared discard bitmap accessed commonly by the host device and data storage device. The shared discard bitmap includes discard bits in one-to-one correspondence with target sectors of a nonvolatile memory device in the data storage device. The method also includes setting bit values of the discard bits stored in the shared discard bitmap, the bit values indicating whether data stored in each of the target sectors are discardable. An asynchronous discard operation may then be performed with respect to the target sectors based on the bit values of the discard bits stored in the shared discard bitmap.