Alice seems to be a little girl, somewhere between eight and ten years old. She's got blonde hair, ridiculously long pigtails and psychic powers that let her do anything. Teleport, either herself or other people? Yeah, sure. Create objects out of thin air? What do you want and where do you want it? She's escaped from a research facility that found her so interesting that they're willing to commit violence to get her back.
You've probably seen this before. Elfen Lied, Brynhildr in the Darkness, etc. The girl will meet a boy and the story will get very dark.
Zouroku is the "boy" in this scenario, but with a difference. He's a grumpy grandfather who works as a florist and has no patience for rudeness, bad behaviour or lack of respect. Throwing cars at him falls into all three categories. He's got no superpowers and you might guess his life expectancy at three minutes, but fortunately he's also cool. You've got to love a cantankerous grandad whose reaction to being attacked by supervillains is to tell them they're being rude. He just wants Alice to go away and stop bothering him, but that's not going to happen.
The story softens. Alice becomes Zouroku's second granddaughter. (His real one is Sanae, a girl so happy and relaxed that you might wonder if she's on drugs. She's also lovely. When she gets cross with Zouroku in ep.4, it's such a gentle scolding that it's like being nibbled by butterflies that have a good point.) Surprisingly the villains stop being a problem halfway through the series, with a second story arc about a nice girl who thinks she's an evil witch. Seeing her story could be a bit sad, but it ends nicely.
The art style's quite simple. I wouldn't quite call it stylised, but it's the kind of character design you might expect to find on something featherlight and fluffy like Nichijou. That's another way in which the show's dark premise is being softened.
I think the first story arc is stronger than the second one. Evil child-kidnapping research centres are always strong villains. The superpower battles are pretty spectacular and it's all good, solid stuff that's exactly what you'd expect it to be. The second story arc is in some ways more interesting, but also less gripping. It's basically an exploration of children's worldviews, with no real villain and a cast of characters who are bad at interacting with other people. Hatori has some weird ideas about why her parents argue. Alice doesn't know how the world works or how she fits into it, but she's come up with an eye-opening theory about what she is.
I liked it. I think it's charming. It also has cute title sequences. It has some dark content, obviously, but it's no "kill 'em all" gorefest and I think Alice, Zouroku and Sanae make it a warm series. Zouroku is my hero.