I think an even better question is "What's up with Enoch and Elijah? Those dudes aren't even dead yet!"
I would say that Christ resides in the "heavenly places" (Ephesians 1:20, 2:6) and is "at the right hand of the Father" (Mark 14:62, 16:19; Acts 2:33, 7:55; Romans 8:34; Hebrews 1:3, 8:1, 10:12, 12:2). This is what the Scripture teaches us.
From the Holy Traditions of the Church, we believe the Most Holy Theotokos resides there as well, having been assumed into the heavens, raised bodily after her Dormition by her Son (see the hymns for the Feast of the Dormition of the Theotokos).
The rest of the saints reside in "Paradise" and rest in Christ, though they await their bodily resurrections. Much of the Church's understanding on Paradise and the abode of the dead can be seen in the non-canonical Gospel of Nicodemus, in which the Harrowing of Hell by Christ on Great and Holy Saturday is recorded. The work even mentions Enoch and Elijah, to answer my own question above.