The development of viable quantum computation devices will require the ability to preserve the coherence of quantum bits (qubits)1. Single electron spins in semiconductor quantum dots are a versatile platform for quantum information processing, but controlling decoherence remains a considerable challenge1, 2, 3, 4. Hole spins in III–V semiconductors have unique properties, such as a strong spin–orbit interaction and weak coupling to nuclear spins, and therefore, have the potential for enhanced spin control5, 6, 7, 8 and longer coherence times8, 9, 10, 11, 12. A weaker hyperfine interaction has previously been reported in self-assembled quantum dots using quantum optics techniques10, 11, 12, but the development of hole–spin-based electronic devices in conventional III-V heterostructures has been limited by fabrication challenges13. Here, we show that gate-tunable hole quantum dots can be formed in InSb nanowires and used to demonstrate Pauli spin blockade and electrical control of single hole spins. The devices are fully tunable between hole and electron quantum dots, which allows the hyperfine interaction strengths, g-factors and spin blockade anisotropies to be compared directly in the two regimes.