Micro-　and　nano-　to　millimeter-scale　magnetic　matrix　materials　have　gained　widespread　application　due　to　their　exceptional　magnetic　properties　and　favorable　cost-effectiveness.　With　the　rapid　progress　in　condensed　matter　physics,　materials　science,　and　mineral　separation　technologies,　these　materials　are　now　poised　for　new　opportunities　in　theoretical　research　and　development.　This　review　provides　a　comprehensive　analysis　of　these　matrices,　encompassing　their　structure,　size,　shape,　composition,　properties,　and　multifaceted　applications.　These　materials,　primarily　composed　of　alloys　of　transition　state　metasl　such　as　iron　(Fe),　cobalt　(Co),　titanium　(Ti),　and　nickel　(Ni),　exhibit　unique　attributes　like　high　magnetization　rates,　low　eleastic　modulus,　and　high　saturation　magnetic　field　strengths.　Furthermore,　the　studies　also　delve　into　the　complex　mechanical　interactions　involved　in　the　separation　of　magnetic　particles　using　magnetic　separator　matrices,　including　magnetic,　gravitational,　centrifugal,　and　van　der　Waals　forces.　The　review　outlines　how　size　and　shape　effects　influence　the　magnetic　behavior　of　matrices,　offering　new　perspectives　for　innovative　applications　of　magnetic　matrices　in　various　domains　of　materials　science　and　magnetic　separation.　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).　(sic)(sic)(sic)(sic)(sic)(sic)(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),(sic)(sic),(sic)(sic),(sic)(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(Fe),(sic)(Co),(sic)(Ti)(sic)(sic)(Ni)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),　(sic)(sic)(sic)(sic)(sic)(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).　(sic)(sic),　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),　(sic)(sic)(sic)(sic),(sic)(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),　(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic).