The HSL Mathematical Software Library started life in 1963 as the Harwell Subroutine Library. It is the oldest mathematical software library to be in continual use, predating the IMSL and NAG libraries. The Library was originally designed for use at the Harwell Laboratory in the UK on IBM mainframes. Over the years, the HSL Library has continually evolved and been developed and maintained by a small research group of numerical analysts at the Rutherford Appleton Laboratory (on the Harwell campus), whose main interest lies in the development of numerical algorithms and their underlying theory and then implementing these algorithms in state-of-the-art software that is made available through the Group’s software libraries. The HSL Library has been extensively used on a wide range of computing platforms, from supercomputers to modern PCs and laptops. 60 years on, the current version of the HSL Library is still widely used around the world and it remains a highly respected source of software for solving large sparse problems. In this talk, I will give a historic overview of the development of the HSL Library in the context of other key mathematical software libraries. I will discuss some of the recent algorithms and software for sparse problems and end by looking to the future of the HSL Library and what we are planning for the coming years.