We briefly describe Cache Blocking for Dense Linear Algebra Algorithms on computer architectures since about 1985. Before that one had uniform memory architectures. The Cray I machine was the last holdout. We cover the where, when, what, how and why of Cache Blocking. Almost all computer manufacturers have recently (about seven years ago) dramatically changed their computer architectures to produce Multicore (MC) processors It will be seen that the arrangement in memory of the submatrices A_(ij) of A is a critical factor for obtaining high performance. From a practical point of view, this work is very important as it will allow existing codes using LAPACK and ScaLAPACK to remain usable by new versions of LAPACK and ScaLAPACK.
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