1. A computer system comprising: A. a plurality of processing nodes, each processing node comprising: i. a memory for storing a plurality of data items in a plurality of storage locations each defined by an address, addresses of memories of all of said processing nodes forming a unitary address space, with addresses of each processing node's memory comprising a portion of the unitary address space, the memory being responsive to memory access requests each for initiating memory access operation in connection with a data item identified in the memory access request; ii. a processor for processing data, the processor generating data transfer requests to initiate a data transfer operation, each data transfer request including a data item location identifier identifying a storage location in one of the processing nodes' memory; iii. a data transfer controller for receiving data transfer requests from the processing node's processor and, for each data transfer request, (a) if the data transfer request's data item location identifier identifies a storage location in the processing node's memory, generating a memory access request to enable the memory to initiate a memory access operation in connection with the identified data item and (b) otherwise generating a message to initiate a remote access operation in connection with another processing node whose memory includes a storage location identified by the data transfer requests' data item location identifier; and B. a communications network for transferring messages generated by said processing nodes to facilitate remote access operations among processing nodes in connection with data transfer requests generated by the processing nodes' respective processors.