The comprehensive command to do all things in the name of the Lord (3:17) is now applied to everyday household relationships. The Lord wants our social relationships to be sanctified. Paul first deals with marriage and family.
Marriage (18-19): Christ issues a duty for the husband and a different duty for the wife. She is to willingly place herself under her husband's authority. And she is to do this because it is fitting in the Lord. Christ is the reason for her submission. As for the husband, he has no right to be a tyrant. Instead, he is to love his wife. Also, he must not harbor any bitterness. Those closest to you can upset you the most, but the Christian man must forbear and forgive.
Family (20-21): The children are directly addressed. They are to obey their parents in all things, because "this is well-pleasing to the Lord." Total ("all") obedience is how children can please the Lord. Christ Himself set an example of this when He was a child (Luke 2:51). The father, on the other hand, must not abuse his authority. He can wrongly cause his children to "lose heart." His God-given role is to train them (Eph. 6:4), not to ruin them. Discipline should be fair and firm (Heb. 12:10-11), and it should come from love (Prov. 13:24).
 These, plus slavery, were common in the first century household. Same groups appear in Eph. 5:22-6:9.
 The imperative "be subject" is also "submit to" (ESV, NKJV, NET). Women are to actively pursue submission, or literally, "place themselves under." This is a willing placement of herself under her husband's authority.
 "As is fitting in the Lord" explains why she submits. This parallels the explanation in 3:20 ("for this is well-pleasing to the Lord") and lines up with the comprehensive scope of Eph. 5:24. The wife submits because it is Christian (not cultural) to do so. This said, God's authority always trumps human authority (cf. Acts 5:29).
 This is why in the church of God there is need for patience, forgiveness, love, etc. (Eph. 4:31-32; 1 Pet. 4:8-9).
 Cf. 3:13. Instead of bitterness, God wants the husband to live with her with understanding (1 Pet. 3:7).
 In this household context, the "children" are young and in need of raising up (cf. Eph. 6:1-4). The duty of married adults is their marriage (3:18-19; 1 Cor. 7:3; 11:3) and the care of their parents (1 Tim. 5:4, 8).