Over the past twenty years, dense linear algebra libraries have gone through three generations of public domain general purpose packages. In the seventies, the first generation of packages were EISPACK and LINPACK, which implemented a broad spectrum of algorithms for solving dense linear eigenproblems and dense linear systems. In the late eighties, the second generation package called LAPACK was developed. This package attains high performance in a portable fashion while also improving upon the functionality and robustness of LINPACK and EISPACK. Finally, since the early nineties, a third generation package which ports LAPACK to distributed memory networks of computers has been underway as part of the ScaLAPACK project.PLAPACK is a maturing fourth generation package which uses a more application-centric view of vector and matrix distribution, Physically Based Matrix Distribution. It also uses an "MPI-like" programming interface that hides distribution and indexing details in opaque objects, provides a natural layering in the library, and provides a straight-forward application interface. In this paper, we give an overview of the design of PLAPACK.