According to the PICS guide: "There should be written procedures describing the actions to be taken upon receipt of a complaint. All complaints should be documented and assessed to establish if they represent a potential quality defect or other issues."

According to (the International Standards Organization) ISO 9000:2015 - Quality management systems — Fundamentals and vocabulary; "Complaint" is the expression of dissatisfaction made to the company that could be related to the product, service, or the complaint handling process itself.

Complaint needs to be conducted and documented as an important part of the QMS system, to comply with current regulations and requirements such as GMP, ISO, ICH, or FDA.
There should be a procedure(s) for complaint handling and recall thus you can comply with almost every regulation. Of course, they have some minor differences between requirements but in general, if you have an effective complaint handling and recall process you will be able to comply with most of the requirements.

According to (the International Standards Organization) ISO 13485:2015 - Medical devices — Quality management systems — Requirements for regulatory purposes; Complaint handling procedures should be documented following applicable regulatory requirements, and include at minimum;

1.  receiving and recording information;

2.  evaluating information to determine if the feedback constitutes a complaint;

3.  investigating complaints;

4. determining the need to report the information to the appropriate regulatory authorities;

5. handling of a complaint-related product;

6. determining the need to initiate corrections or corrective actions.

If any complaint is not investigated, justification shall be documented. Any correction or corrective
action resulting from the complaint handling process shall be documented.

If an investigation determines activities outside the organization contributed to the complaint, the relevant information shall be exchanged between the organization and the external party involved.
Complaint handling records shall be maintained.

Complaints might be integrated with other QMS processes to track processes more organized and systematic way. It can be integrated into event management, CAPA management, risk management, supplier management, and so on.