In some embodiments, each matrix processor in a matrix of mesh-interconnected matrix processors includes an instruction processing pipeline, and a hardware data switch capable of streaming data to/from one or more inter-processor matrix links and/or a matrix processor local memory links in response to execution of a data streaming instruction by the instruction processing pipeline. The data switch can transfer each data stream, which includes multiple words, at wire speed, one word per cycle. After initiating a data stream, the processing pipeline can execute other instructions, including streaming instructions, while a stream transfer is in progress. Different data streaming instructions may be used to transfer data streams from local memory to one or more inter-processor links, from an inter-processor link to local memory, from an inter-processor link to one or more inter-processor links, and from an inter-processor link to one or more inter-processor links and synchronously to local memory.