And forgive us our debts, as we forgive our debtors. Matthew 6:12
For if ye forgive men their trespasses, your heavenly Father will also forgive you: But if ye forgive not men their trespasses, neither will your Father forgive your trespasses. Matthew 6:14-15
Forgiving those who have wronged us is not a suggestion, but a requirement from God. He demands we forgive. . . just as he forgives us. Forgiving others is what Christians do, it is a virtue of the highest order. Read Proverbs 19:11 It follows the example of Christ and frees our conscience from guilt and bitterness.
To forgive someone is to relinquish the desire to avenge yourself (the desire to hurt someone for hurting you). It is not ignoring or forgetting that you have been wronged. This is not giving up a desire to see justice served but instead leaving punishment in the hands of God. Forgiving is really to our own benefit as we no longer carry anger, bitterness, resentment, or the burning desire for revenge. God tells us that he will take care of the punishment due to them, but that we are to love our enemies!
Recompense to no man evil for evil. Provide things honest in the sight of all men. If it be possible, as much as lieth in you, live peaceably with all men. Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord. Therefore if thine enemy hunger, feed him; if he thirst, give him drink: for in so doing thou shalt heap coals of fire on his head. Be not overcome of evil, but overcome evil with good. Romans 12:17-21
Paul tells us in the verses above that, if possible, we should be at peace with all men. The offer of forgiveness is up to you; acceptance of forgiveness and reconciliation is up to the other party. So do your part and rest in the peace of God.
Also, do not find joy in the misery of others. When those who have wronged us fall, or receive the punishment they deserve, we should not find happiness in that. We should have compassion for them, as difficult as that may be. Read Proverbs 24:17