There are over 20 peaks more than 3,000m, which makes it the second highest mountain range in Europe after the Alps. The two highest peaks in the Iberian Peninsula are in the park, the Mulhacén at 3,482m, closely followed by the Pico del Veleta, at 3,396m. On a clear day these mountains can be seen from as far away as Africa.

The park has a rich history, with the Tartessians, Visigoths, Romans and Moors all leaving their legacy in the area, which can be still be seen today; for example, the sophisticated irrigation systems inherited from the Moors and the distinctive architecture of the Alpujarras, with their flat-roofed houses, a design brought from north Africa with the Berbers.

The Alpujarras have a long tradition of independence; the last Moorish king, Boabdil, famously sheltered here after the fall of Granada. It became the Moors' last refuge in Spain before their 1568 revolt failed and they were forced to leave Spain.