Once an FIR has been filed the police are legally bound to start investigating the case.
The process of investigation includes, but is not limited to, collecting evidence, questioning witnesses, inspecting the crime scene, forensic testing, recording statements and so on. If the criminals are found, the police will make arrests.
Once the investigation has been concluded the police will record all their findings in a ‘Challan’ or charge sheet. If it is deemed that there is enough proof on the charge sheet the case goes to court.
On the flipside, after their investigations if the police conclude that there is not enough evidence or proof that a crime has been committed they can close the case after justifying their reasons in court. If the police decide to close the case, they are bound to inform the person who filed the FIR of their decision.