AT:

1. Enhancements of the process instance query

I can query for process instances by incidentType:

runtimeService.createProcessInstanceQuery()
.incidentType(...)

I can query for process instances by incidentID:

runtimeService.createProcessInstanceQuery()
.incidentId(...)

I can query for process instances by incidentMessage:

runtimeService.createProcessInstanceQuery()
.incidentMessage(...)

1. Enhancements of the execution query

I can query for executions by incidentType:

runtimeService.createExecutionQuery()
.incidentType(...)

I can query for executions by incidentID:

runtimeService.createProcessInstanceQuery()
.incidentId(...)

I can query for executions by incidentMessage:

runtimeService.createExecutionQuery()
.incidentMessage(...)

1. Enhancements of the process definition query

I can query for processDefinitions by incidentType:

repositoryService.createProcessDefintionQuery()
.incidentType(...)

I can query for processDefinitions by incidentId:

repositoryService.createProcessDefintionQuery()
.incidentId(...)

I can query for process definitions by incidentMessage:

repositoryService.createProcessDefinitionQuery()
.incidentMessage(...)

1. REST Api enhancements

All enhancements listed above should be added to the REST Api as well.