Call recording is a feature that records the content of a phone call as audio data. Businesses use it for call center quality management, compliance, and establishing what was said when a problem arises; individuals use it to keep a record of nuisance calls or threatening calls.
Whether you may record, and how far you may use the audio afterwards, depends on the purpose of the call, your relationship with the other party, and whether the recording leaves your hands. Because no blanket judgment on whether a particular situation is lawful can be made here, consult a lawyer or another specialist for recordings tied to a dispute or where the audio may be shown to a third party. Announcing in advance that "this call may be recorded for quality improvement," as call centers commonly do, is a widely seen practice: telling the other party that recording is under way reduces the occasions on which the existence of a recording later becomes a point of friction.
What you can record on a smartphone depends on the OS and on app distribution rules. On Android, third-party app call recording has been progressively restricted over time, and whether a built-in recording feature is available differs by device manufacturer and by region. Handling also varies on iPhone by OS version and region, so the reliable approach is to check whether recording works on the handset in front of you. If the device itself cannot record, options include an external recording adapter, or placing and receiving calls through a calling service that provides recording.
For business use, some cloud PBX services build call recording in. Some of them record every call automatically and store it in the cloud so it can be searched later, which helps prevent disputes over what was said and provides material for training new staff. Call centers may operate by sampling recordings for review to gauge the quality of their responses. What tends to be overlooked in practice is that a recording can exist and still be impossible to retrieve when needed, because there is no record of when the call took place or which number it involved. Setting internal rules on whether the date, time, and counterpart number are stored alongside the audio, who may play it back, and how long it is retained saves confusion later. See Legal Rules and Practical Uses of Call Recording for a fuller treatment that includes the legal side.