The concept of repentance, as taught in modern Christian denominations, can often elicit some form of controversy or confusion, largely because it ostensibly contradicts the solas doctrine, especially solus Christus and sola gratia. If Jesus Christ is the sole proprietor, author, and perfector of our faith (Heb. 12:2), then it's somewhat paradoxical for the mandate of repentance to be inscribed in Christian dogma. Many who grow up in the church will likely hear things like: "You must repent before entering the kingdom of heaven" and like phrases. This was indeed one of the preeminent challenges to my understanding of theology-- how could we be saved wholly reliant on God's grace but still fail to enter His kingdom by omission of repentance?
I believe repentance, actually, is taught incorrectly in modern Protestant denominations. The reason why the aforementioned paradox appears to be a contradiction is largely how repentance is framed. It is commonly held that repentance essentially means permanently refraining from committing a sin or multiple sins that were persistent in one's life. Indeed, when not expounded upon, it sounds like repentance essentially demands that one stops sinning entirely. The fatal flaw is that this diminishes the value of repentance to works, an action that we ourselves can take and have control over. When fit into the clause: "one must repent to enter the kingdom of God," then we are left with a statement that says salvation is to be earned through work. From scripture, we know this is entirely incorrect.
Because salvation through grace is not earned from works, or earned at all in fact, it is impossible and contradictory to teach repentance both as a prerequisite for salvation and as something that constitutes a body of works. So what is repentance? Repentance is an entirely God-given fundamental adoption of the new and living way (Heb. 10:20), an alteration of worldview so that the operation of living is no longer done for one's selfish and sinful purposes of pleasing the flesh, but done entirely in submission to God and His glory. In other words, you are no longer living for sin and the world (in essence, our life out of the first Adam) but now living for His kingdom (life given by Christ, the second Adam), as an adopted child of God.
Repentance, then, is not the eradication of sin out of life but the transformation from a life enslaved by sin to a life enslaved by God (more on this later). As a result, it should follow that a repentant heart will also yield the effect of sin being less and less apparent in his or her life. Above all, repentance is a process completely authored by God and only possible through His grace. We can never incline ourselves to repent without the initiation of God's love first. As we recognize that, then can we begin to undergo the true transformation of repentance.