Hupo (ὑπό) is one of the fundamental Greek prepositions, expressing: (1) position under — beneath, below, subject to; (2) agency — by/through (especially in passive constructions: 'raised by God'); (3) subjection — under the authority or power of another. It appears hundreds of times in the NT and is grammatically crucial for identifying the agent in passive verbs.
Theologically, hupo carries enormous weight in several key texts. Galatians 3:23-25: 'we were held captive under the law' — then Christ came to redeem 'those who were under the law' (4:5). The condition of humanity is hupo — under sin (Romans 3:9), under the law, under condemnation. Christ's mission is liberation from every hupo that enslaves. 1 Corinthians 15:27: 'he has put all things in subjection under his feet' — the eschatological hupo of all enemies beneath Christ's authority, including death itself. Philippians 2:10: 'every knee shall bow, things in heaven and on earth and under the earth' — the cosmic submission that hupo names.
The movement of redemption is from 'under' to 'over' — from slavery under sin and death, to co-reigning with Christ (Revelation 20:6; Romans 8:17). Jesus himself was born 'under the law' (hupo nomon, Galatians 4:4) to redeem those under the law. The preposition that marks captivity is the same one that marks the entry of the Liberator: He came under the very thing He came to remove, sharing our condition to transform it. This is the logic of incarnation.