Here is my first post about discovering K-drama (Korean dramas, in case you weren't in-the-know)(I wasn't in-the-know until a few months ago, so don't feel bad).
And here are some more shows I can highly recommend:
Goblin: Love the fantasy premise of this one and the way it's played out. A betrayed general is cursed to become an immortal goblin. 400 years later he's sharing a house in modern Seoul with a Grim Reaper (lovely irony), using his powers for good and searching for the Goblin Bride, the only one who can grant him death. Of course, when he finally finds her, he falls in love with her. Funny and poignant, with great acting, gorgeous scenery (nice use of Quebec City as a romantic backdrop), and interesting things to say about fate, free will and messing with what's meant to be.
Healer: Reminds me a bit of Arrow, except cuter (both show-in-general and lead actor!). Kick-ass martial arts expert does shady deliveries for people who don't like questions, until one job leads him to a girl struggling to make it as a reporter. They are both connected to a wrongful death from the past, and Healer might be willing to go straight if it means he can protect her. Fun action, adorable romance, and another great performance from Kim Mi Hyung, who was my favourite character in Faith (The Great Doctor).
Kill Me, Heal Me: Fantastic acting in this story of a chaebol (wealthy corporation) heir with multiple personality disorder. One of his personalities falls in love with a girl (who happens to be a psychiatrist), and things start to get complicated. This is one of my favourite dramas I've seen so far. It is a treat to watch Ji Sung play five different personalities, and then play the main persona changing as he integrates each personality. Sounds serious but there's a lot of humour.
Sungkyunkwan Scandal: this one is just so fun and cute I never wanted it to end. Girl dresses up as a boy and gets into the Sungkyunkwan Academy. Hijinks ensue. There's romance (of course) and people plotting against the king (of course), and Song Joong Ki, who is reason enough to watch anything.