An apparatus comprising: processing circuitry to perform data processing operations in response to program instructions; trace circuitry to output exception trace data indicative of exception handling events detected during monitoring of processing activity of the processing circuitry; and a configuration element to maintain exception trace configuration data for controlling the output of the exception trace data by the trace circuitry; wherein: when output of the exception trace data is enabled, the trace circuitry is configured to select, in dependence on the exception trace configuration data, how much of the exception trace data to output; the exception trace data comprises one or more exception trace packets; and the trace circuitry is configured to select, in dependence on the exception trace configuration data, whether to include an exception identifier in at least one exception trace packet, the exception identifier identifying an exception type for which an exception handling event occurred, said at least one exception trace packet having one of a plurality of encoding formats, the plurality of encoding formats including a first format in which the exception trace packet includes the exception identifier, and a second format in which the exception identifier is omitted from the exception trace packet. processing circuitry to perform data processing operations in response to program instructions; trace circuitry to output exception trace data indicative of exception handling events detected during monitoring of processing activity of the processing circuitry; and a configuration element to maintain exception trace configuration data for controlling the output of the exception trace data by the trace circuitry; wherein: when output of the exception trace data is enabled, the trace circuitry is configured to select, in dependence on the exception trace configuration data, how much of the exception trace data to output; the exception trace data comprises one or more exception trace packets; and the trace circuitry is configured to select, in dependence on the exception trace configuration data, whether to include an exception identifier in at least one exception trace packet, the exception identifier identifying an exception type for which an exception handling event occurred, when output of the exception trace data is enabled, the trace circuitry is configured to select, in dependence on the exception trace configuration data, how much of the exception trace data to output; the exception trace data comprises one or more exception trace packets; and the trace circuitry is configured to select, in dependence on the exception trace configuration data, whether to include an exception identifier in at least one exception trace packet, the exception identifier identifying an exception type for which an exception handling event occurred, said at least one exception trace packet having one of a plurality of encoding formats, the plurality of encoding formats including a first format in which the exception trace packet includes the exception identifier, and a second format in which the exception identifier is omitted from the exception trace packet.