Fomalhaut30: Gate - Story about a medieval fantasy world finding a magical gate that brings them to current day Japan. They send an invasion force through with predictable results. Japan sends an expeditionary force through the gate. Predictable results of bringing swords to a gun fight. Main character is an otaku slacker in the JSDF. Currently ongoing and on Hulu.
Is It Wrong To Try To Pick Up Girls In A Dungeon - Story about a guy who is trying to become a dungeon adventurer. Every adventurer joins a familia (family) of a god or goddess. He's the only one in his familia. Has a handy way of explaining how lots of people can adventure in the same dungeon without running out of baddies to defeat. First season is finished. Don't know if there'll be more. Available on Hulu.
Older but if anyone likes these two I'd recommend
Outbreak Company (premise is a lot like Gate but rather than a military invasion they use a cultural approach (ie, they find the biggest otaku and send him through to teach them all about otaku culture, you can see where this is going)
And
No Game No Life
No Game No Life is a surreal comedy that follows Sora and Shiro, shut-in NEET siblings and the online gamer duo behind the legendary username "Kuuhaku." They view the real world as just another lousy game; however, a strange e-mail challenging them to a chess match changes everything—the brother and sister are plunged into an otherworldly realm where they meet Tet, the God of Games.
The mysterious god welcomes Sora and Shiro to Disboard, a world where all forms of conflict—from petty squabbles to the fate of whole countries—are settled not through war, but by way of high-stake games. This system works thanks to a fundamental rule wherein each party must wager something they deem to be of equal value to the other party's wager. In this strange land where the very idea of humanity is reduced to child’s play, the indifferent genius gamer duo of Sora and Shiro have finally found a real reason to keep playing games: to unite the sixteen races of Disboard, defeat Tet, and become the gods of this new, gaming-is-everything world.
I should probably try out food wars. I managed to sit through Yakitate Japan! so I should be able to manage this one:)