A periphrasis with εἰμί and a (usually mediopassive) perfect participle signals a resultative aspect.
Εἰμί + perf. part. replaces the perfect; ἦν + perf. part. replaces the pluperfect. In the third person plural of the mediopassive perfect and pluperfect indicative the periphrastic form is the only form to occur when the verb ends in an occlusive. The perfect subjunctive and optative are always periphrastic.
The future perfect active is always periphrastic with ἔσομαι + perf. part., except in cases such as ἐστήξω 'I will stand up' or τεθνήξω 'I will be dead'.
This is the oldest periphrastic verb tense in Greek, already occurring in Homer.