A data processing apparatus has at least one circuit block accessible for debugging by a debugger, the block having a set of debug status registers and a debug event register which is set by the circuit block to indicate occurrence of a debug event. Debug interface circuitry interfaces with the set of debug status registers for each circuit block. The circuitry includes at least a first portion which is in a first power domain that remains in a fully powered state whilst the debugger is connected to the circuitry. Status registers are provided in a second power domain which transitions between the fully powered state and at least one low power state whilst the debugger is connected to the circuitry. Content of the debug status registers is only accessible to the debugger when the second power domain is in the fully powered state.