Dude I've been playing slot of Karthus lately. He's very underrated. His level 1-3 is stupidly powerful because his Q does double damage if it hits one target (I'm sure you know that). Also his E restores Mana on kill so it's like Annie, with Better range and a shorter CD. While his ult dmg is relatively weak, he can be very tanky and shreds with his Defile. If paired with Soraka or another healer he is even more deadly. If they have a lot of tanks throw your W down because it reduces their MR as well as their speed. You can play him as a DPS backline with your Q's or get in the fight and peel for everyone because the enemy is like "ow this defile wtf kerthos pls". Grab a rylais and abyssal mark and boom, they slow af and take 10% more magic damage. Lately I've been playing DPS Mage Karthus and the enemy either focuses me or tries to run off.
Karthus is actually a strong pick against melee as well especially Yasuo, because if he wants to trade with you, just toggle defile and start throwing Q's on top of yourself. He will either eat them or try to avoid them and miss harass/farm because he's spending too much time avoiding your Q's (still taking dmg from defile). Once he backs off throw your W down and get free double dmg Q's.