The Other Three Compound Tenses
There are one other indicative and two subjunctive compound conjugations: The Past Anterior or Preterite Perfect is not used much in spoken Spanish. It expresses past action and is used mostly in literature after verbs of time. Many Spanish speakers don't even learn this conjugation. For information, this tense uses the following forms of haber: hube, hubiste, hubo, hubimos, hubisteis, hubieron.
The other two compound tenses are the present and the past perfect subjunctive. These subjunctive tenses are likewise formed by adding the conjugated form of haber to the past participle:
Present Perfect Subjunctive: haya, hayas, haya, hayamos, hayáis, hayan.
Past Perfect Subjunctive: hubiera, hubieras, hubiera, hubieran
The subjunctive compound tenses are used when there is a situation requiring the subjunctive and needs the present or past perfect. Some examples of the subjunctive construction:
Present subjunctive: Maria duda que yo le haya hablado al professor. Mary doubts that I have spoken to the professor.
Past subjunctive: No creía que María hubiera hablado. I did not believe that Mary had spoken.
To read more about the subjunctive mood.