Over the past twenty-five years, we have been involved in the development of several important packages of dense linear algebra software: EISPACK [24][36], LINPACK [16], LAPACK [1], and the BLAS [18][19][28]. In addition, we are currently involved in the development of ScaLAPACK [8], a scalable version of LAPACK for distributed memory concurrent computers. In this section, we give a brief review of these packages-their history, their advantages, and their limitations on high-performance computers.