
die Verfolgung
pursuit
Chasing or running after someone or something in order to catch up with or capture them or it.
Die Polizei nahm sofort die Verfolgung des Fluchtautos auf.
The police immediately took up pursuit of the getaway car.
pursuit / persecution
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pursuit
Chasing or running after someone or something in order to catch up with or capture them or it.
Die Polizei nahm sofort die Verfolgung des Fluchtautos auf.
The police immediately took up pursuit of the getaway car.

persecution
The systematic oppression, discrimination, or mistreatment of people or groups because of their political, religious, or ethnic affiliation.
Die politische Verfolgung in seiner Heimat zwang ihn zur Flucht.
Political persecution in his homeland forced him to flee.

prosecution
The legal punishment or pursuit of a criminal offense by the competent authorities such as the police and public prosecutor's office. Often used in the term 'Strafverfolgung' (criminal prosecution).
Die Verfolgung von Steuerhinterziehung wurde in den letzten Jahren intensiviert.
The prosecution of tax evasion has been intensified in recent years.

pursuit / tracking
The consistent pursuit of a goal or the observation of a process.
Die Verfolgung seiner beruflichen Ziele hat sich für ihn ausgezahlt.
The pursuit of his professional goals has paid off for him.
The noun 'die Verfolgung' (pursuit / persecution) comes from the verb 'verfolgen' (to pursue / follow). This verb consists of the prefix 'ver-' and the verb 'folgen' (to follow). The basic meaning of 'following someone or something' can be recognized in all meanings of the noun.
Die Fans verfolgten das Spiel mit großer Spannung.
The fans followed the game with great excitement.
To say who or what is being pursued, the genitive or the preposition 'von' is usually used. The genitive is more common in written language.
Die Verfolgung des Täters dauerte mehrere Stunden.
The pursuit of the perpetrator lasted several hours.
In the context of a chase or escape, the fixed expression 'die Verfolgung aufnehmen' (to take up pursuit) is often used. It means that you begin chasing someone.
Nach dem Banküberfall nahm die Polizei sofort die Verfolgung auf.
After the bank robbery, the police immediately took up pursuit.
This meaning is often recognizable from adjectives like 'politisch' (political), 'religiös' (religious), or 'ethnisch' (ethnic). The context is usually historical or has to do with human rights.
Viele Künstler mussten wegen politischer Verfolgung ihre Heimat verlassen.
Many artists had to leave their homeland because of political persecution.
In legal contexts, the word 'Strafverfolgung' (criminal prosecution) is often used. It refers to the work of the authorities that investigate and punish a criminal offense.
Die Strafverfolgung von Internetkriminalität ist eine große Herausforderung.
The prosecution of cybercrime is a major challenge.
When it is about achieving something abstract, 'Verfolgung' (pursuit) is often combined with nouns such as 'Ziele' (goals), 'Träume' (dreams), or 'Interessen' (interests).
Die konsequente Verfolgung ihrer Ziele führte sie zum Erfolg.
The consistent pursuit of her goals led her to success.
hunt / chase
Both words can describe intensely following a person or thing. „Verfolgung“ describes this process more neutrally, while „Jagd“ emphasizes the focused, often confrontational or hectic search more strongly. Use „Verfolgung“ for an objective description; if the tension or combative pursuit should be apparent, „Jagd“ is appropriate.

Die Verfolgung des flüchtenden Diebes dauerte bis in die Nacht.
The pursuit of the fleeing thief lasted into the night.
Die Jagd nach dem flüchtenden Dieb dauerte bis in die Nacht.
The chase after the fleeing thief lasted into the night.