Man-marking predates zonal marking and still appears in modern football, especially on set pieces or on creative number 10s who need to be silenced.
The upside is clarity: you always know who you are chasing. The downside is that a skilful opponent can drag you out of shape, creating space in behind or in midfield.
Hybrid systems mix zonal and man-marking: a low block defends zones while one or two defenders track a specific star. Atlético under Simeone have used variants of this for years.