• 悔くいる — to feel remorse; to repent
• 悔くやむ — to regret; to mourn a loss
• 悔くしい — vexing; frustrating; bitterly regrettable
• 後悔こうかい — regret; remorse about the past
• 悔悟かいご — deep repentance; awakening with regret

悔 combines the “heart” radical 忄 with a component that hints at the sound カイ. The meaning grows from the idea of a heart that cannot settle, looking back again and again on what has already happened. In modern Japanese it is strongly tied to feelings of regret and repentance.