Here non-natives to Earth (including non-native humans) and their descendents are known as Shadowkind. There's a "veil" that makes most normal people see semi-normal (though often on the very end of "normal") things when looking at the various fantastic races. When Shadowkind die, their bodies dissolve within seconds (most) or hours (heroic individuals). Most are stranded on Earth since planar travel from Earth doesn't work in this setting (one character in a sample adventure is capable of bringing things in on demand however). Normal people overtly exposed to Shadowkind acting abnormal multiple times quickly become immune to the veil.
A group known as Department-7 exists that is dedicated to studying the shadow and helping non-evil Shadowkind. The details (all of them) of this organization are left for the GM to customize, though it's assumed the PCs are likely to work for them shortly into their careers.
Not all Shadowkind are friendly. Many evil monsters have entered the world through the incoming planar tide and have adapted their schemes to this new world. Orcs become gangbangers, Drow run seedy nightclubs and the most brutish monsters just rampage if they aren't first coerced into working as enforcers for other monsters. Certain entities from the Shadow are able to exert some kind of influence onto Earth, though this largely amounts to granting spellcasting and orders to minions.
Magic had adapted to the modern era. The "Techno Mage" class records spells digitally instead of on paper, can design simple devices or programs to cast a spell when activated (mechanically potions), create AI homunculus and cast spells through the phone or internet.