It Still Confuses Me: Who can receive Communion where (Catholic/Orthodox)? I'm fairly well versed on the political history of the Great Schism of the 11th century; however, I can't seem to get it straight when it comes to appropriate receiving of Communion.

Now, I've never seen a priest pull back his hand and say, "Forget it; today you get a blessing," even someone smelling of alcohol. So in practice, assuming one is not committing heresy, at worst receiving Communion inappropriately can be rectified through an act of contrition.

But how is it really supposed to work? I'm Roman Catholic. Can I legitimately go to my friend's Greek Orthodox church and receive Communion?  What about my Russian neighbor baptized Eastern Orthodox? Can he receive Communion at my church? If restricted, is there a permission process outside of RCIA (Rite of Christian Initiation in Adults)?

Were the answers to the above questions identical before the schism, and if not, how?
The Catholic Church permits the Orthodox to receive the Eucharist in a Catholic service, but cautions them to observe their own disciplines. For example, OSCCB offers:


  Members of the Orthodox Churches, the Assyrian Church of the East, and the Polish National Catholic Church are urged to respect the discipline of their own Churches. According to Roman Catholic discipline, the Code of Canon Law does not object to the reception of Communion by Christians of these Churches (canon 844 §3).


The Catholic Church permits a Catholic to receive in an Orthodox service if a Catholic service is not available:


  Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.(canon 844 §2)


The appropriate sections of the canon law can be found here.

According to the Orthodox Church, the Orthodox may not receive the Eucharist in a Roman Catholic Church. For example, the OCA offers this answer:


  Further, Orthodox Christianity does not permit its faithful to receive Holy Communion in non-Orthodox communities, whether they be Roman Catholic, Protestant, or whatever. Hence, while Roman Catholicism may extend Eucharistic hospitality to Orthodox Christians, it does not mean that Orthodox Christians are permitted to accept such hospitality.


Further, non-Orthodox can not receive in an Orthodox service:


  Because a non-Orthodox individual has chosen not to embrace all that Orthodox Christianity holds, the non-Orthodox individual makes it impossible for an Orthodox priest to offer him or her communion. 


Before the Great Schism, there was no formal separation between East and West.