Whether the individual is wanted for a criminal investigation or arrest, or the person of interest is already under probation that is supervised either by the court (informal) or by a probation officer (formal), there are different types of warrants a court orders that allows law enforcement to seize an individual and bring them before the court.
Police may obtain a search warrant to search either a person, car, residence, or business if they have probable cause, and a judge approves of the facts stated in the officer's sworn affidavit that there is enough under the Constitution to issue the warrant.
Officers may also obtain a court approved warrant to arrest an individual if the police have stated articulable facts that amount to probable cause to arrest someone. As in search warrants, the judge that grants the request from law enforcement must assess whether or not the warrant complies with Constitutional safeguards and standards. A defective warrant to arrest someone can be challenged in court and ultimately cause the suppression of evidence that would essentially nullify the prosecution's case.
Ordinarily in cases of probation violations or non-appearances by defendants, the court may issue a warrant for someone's arrest where there has either been an allegation that the person is in violation of probation or there is some other issue that determines the person should be before the court.