Both　information　divergence　and　distance　are　measures　of　closeness　of　two　quantum　states　which　are　widely　used　in　the　theory　of　information　processing　and　quantum　cryptography.　For　example,　the　quantum　relative　entropy　and　trace　distance　are　well　known.　Here　we　introduce　a　number　of　new　quantum　information　divergence　and　distance　measures　into　the　literature　and　discuss　their　relations　and　properties.　We　also　propose　a　method　to　analyze　the　properties　and　relations　of　various　distance　and　pseudo-distance　measures.