I've been putting a lot of time into
Dragon Village M lately.
It's basically a game of watching your team of dragons trade fireballs with waves of enemies, and occasionally intervening to spend some mana for a power-move. The power-moves can also be left to auto-play if desired, and the AI is usually sufficient for most grinding purposes.
The bulk of actual human intervention comes in the form of strategic preparation; sifting through piles of newly hatched dragons, studying their active and passive skillsets, and deciding which ones to throw into your active teams immediately, which ones to save for later, and which ones to sacrifice as fodder to empower other dragons.
Dragon Village M also borrows the Runes system pioneered(to the best of my knowledge) by Summoner's Wars. This is something I've actually seen incorporated into a large number of games lately. For those unfamiliar, these runes essentially act as equipment from any other RPG, boosting your unit's stats directly and also through set bonuses. What stands out about the rune system is that specific rune slots and sets can be acquired from specific story levels, making it relatively simple to farm the pieces you want in order to min-max your units. It creates a good balance of grinding and progression, so that you can see your units getting noticeably stronger after almost every battle.
Dragon Village M does have a cash-shop, but it is extremely generous with the rewards from daily quests and regular events, allowing free players to effectively compete with whales with only moderate time and effort invested.
I've also been playing a bit of
Honkai Impact 3rd.
This is an action game, and easily the best I've seen on a mobile device. Both in terms of graphics and gameplay, it's as good as they come.
Gameplay involves mashing the attack button in combos which vary between different characters, timing a dodge-button to avoid damage and launch a counterattack, accumulating mana for power-moves, and swapping between active characters to take advantage of a paper-rock-scissors systems.
There are a variety of characters to unlock, level, equip, and learn their movesets. Regular events to farm, lengthy story mode to explore.
There's also fan-service, with all of the characters being female, and most wearing skin-tight outfits with plunging necklines. You've been warned.