This is difficult country for travel; the great 14th century Moroccan traveller Ibn Battuta said the name meant "Hindu killer", going back to the days when slaves taken in the subcontinent were brought to market in Central Asia via the Salang Pass and many died during the trek.
Most of the range is in northern Afghanistan; Band-e Amir National Park and the Afghan province of Nuristan are located within the Hindu Kush. The Wakhan Corridor leads from this range up into the Pamirs and to the Xinjiang autonomous region of China.
Other parts of the range are in Pakistan; the highest mountain of the Hindu Kush at 7708 m is Tirich Mir in the Chitral district.
A hilarious and informative book about the area is Eric Newby's A Short Walk in the Hindu Kush; when Newby and a friend visited Nuristan in the 1950s, they were the second or third European expedition ever to reach it. Another book about the area is Joseph Kessel's The Horsemen, a fantastic read.