Into its third week, Batwoman has been on unsteady footing thus far. The show is trying to establish a bunch of characters and an unfamiliar version of a place we're very familiar with. It's a tough task. In week 3, the writers seem to have finished the groundwork and are finally ready to do some Caped Crusading. Spoilers for Batwoman season 1, episode 3, titled "Down, down, down" follow.

"Down, down, down"

In her quest to find and rescue her sister, Kate Kane donned the Batman outfit and put her extensive combat training to work. She stopped Alice, but in the process, she also told Gotham that Batman is alive and well. Batman, who had been missing for three years, is back. As Alice says, Gotham is now "horny for Batman." That's poetry.

Again, the relationship between Alice and Kate is at the center of this story, and I hope that doesn't change because Alice is great. She's tough to read in the best possible way.

We see who Alice really is when she's alone. She's conflicted. A memory of her as a child, as Beth, shows her finding a murky sink in an unknown basement. A face floats to the top. Not an entire head, though; just the face. I think the idea here is that after Beth disappeared in that crash, she went through some nasty stuff that caused her to bury the Beth persona and create the Alice one as a way of surviving. I wonder how she'd like Crazy Jane.

Later, we see her wandering around Jacob Kane's penthouse, having killed the guard and made her way into the secure location almost casually. There, she taunts Jacob, playing Beth's favorite song on a cello over the phone. It's theatrical without being Too Much. Then she digs through some of Kate's boxes and finds the map of all the places Kate searched for her, including the farm where her bone fragments were supposedly found.

Rachel Skarsten does some good subtle work here. The map throws into doubt the assumption that her entire mission is built upon; Kate really did look for her - extensively.

This conflict plays out at the end of the episode, but we'll get there.

Tommy Boy

While Alice is questing and questioning, a name that will be familiar to Batman fans gets a face in Batwoman. Bruce's old friend Tommy Elliott is back in town, and he's richer than Bruce. He even bought a taller building so that he can look down on the Wayne tower. You might know Tommy as Hush. He doesn't wrap his face in bandages here, but he definitely has a vendetta.

It seems that on top of his rivalry with Bruce, Tommy has already figured out that Bruce is Batman. And Batman saved one of his parents, saddling the young man with the responsibility of taking care of his ailing mother for over a decade. Elliott resents Batman in particular for that. With Batman back in town, he wants to collect on his revenge.

It's a proper supervillain plot, too. To celebrate his return, Elliot throws a party for Gotham's elite, and then traps them in elevators that he has rigged to drop countless stories unless his old friend Batman shows up. And Elliott just happens to have stolen a railgun from WayneTech that is powerful enough to penetrate Batman's armor. We'll put aside the myriad problems with that technology, though.

Kate has been arguing with herself about her responsibility to Gotham. She never meant to become Batwoman. She opened the door, not realizing the storm of metaphorical bats about to pour out. And now, she can't put the bats back; she has to deal with the consequences of her actions.

In the episode's final scenes, Kate spraypaints the bat symbol red and attaches a bright red wig to the cowl for her big reveal. She faces down Elliott and defeats him rather handily, though Elliott's planning accounts for everything except Alice showing up with a bat and not announcing herself before clobbering him from behind. Kate uses more of Bruce's gadgets to save a second falling elevator, and ultimately see Elliott arrested. We all know that arrest is just a speedbump for the rich, though, and Elliott is obscenely wealthy. He'll be back, and now he's pissed at two members of the Bat-Family. With Elliott unconscious, Kate has a moment to talk to Alice, and the tension between them is palpable. Alice definitely isn't an ally, but she's not exactly an enemy, either.

In the background

In the background, other relationships are developing. Kate flirts with a very perceptive bartender in front of her ex-girlfriend Sophie. Sophie, it turns out, hasn't told her husband about her prior relationship with Kate. Sophie gets herself assigned to act as a bodyguard for Kate's step-sister Mary, whose doctor instincts force her to out herself as something other than a socialite airhead in front of Sophie. Kate's step-mother, Catherine, comes home to find a set of 3 cards on her desk (2, 3, 8), left by our good friend Alice. Catherine hides them quickly. I have a feeling she's the true villain of this storyline, while Alice is the tragic one.

There are some great moments throughout, too. We get our first earful of Vesper Fairchild, the character played by Rachel Maddow. Vesper is a frequent character and sometimes lover of Bruce in the comics, though it's unclear here if they had any prior relationship, as Vesper seems much more interested in Batwoman. We have a short scene with Sophie and her husband sparring at Crow headquarters in the worst-lit gym I've ever seen. There's someone pumping iron in the dark. That's dangerous! And then Tommy calls Kate's previous training a "Lesbian Ninja Retreat." I do have to call out the not-great green-screen effects from the end of the episode here. I know the CW is working on limited funds. I can't help but wonder if Batwoman's black suit against the night sky ended up presenting unique challenges fo the camera and VFX teams.

"Down, down, down" left me more excited than ever for Batwoman's freshman season. We know the Riddler exists. Hush is brewing. Alice is fascinating. There's a ton of space to play in. And it seems like the show is determined to never confirm that Batman is dead, so we can hold out hope for a live-action Batman. Until then, Batwoman is getting better and better.