Plance

Plance is the Het ship between Lance and Katie Holt from Voltron: Legendary Defender. It has a decent following on various social media platforms, and has recently come out of rarepair status. The two characters are some of the only ones shown to blush in the show, and blush at each other various times. It is implied that Pidge might have a crush on Lance. However, this is currently unrequited as Lance has a crush on Allura.

Canon
Pidge and Lance met at the Galaxy Garrison approximately a year before the show's events take place. Pidge is assigned to Lance's team, along with Hunk, and Lance is friendly when greeting her. She brushes him off, though, since she is only here to find information about her missing brother and father. In the show's first episode, Lance and Pidge are shown arguing while in a flight simulator, with Pidge seemingly annoyed at Lance's cockiness. Despite all this, however, Lance obviously still considers Pidge a friend. He stops her from speaking out against their professor, choosing to take the commander's wrath himself. Later, when he and Hunk are sneaking out for a night on the town, Lance makes a point to go get Pidge first, and follows her when she sneaks onto the roof. It is here that we see that their relationship has grown a little since they've first met--Lance is comfortable with sneaking up on her, teasing her, questioning her and being in her personal space, and Pidge doesn't seem to hold any of it against him. Also, despite being skeptical of her claim she about aliens, Lance excitedly follows Pidge when she runs to check out the unidentified object that falls from the sky.

After they find the blue lion and are about to go into a wormhole, Lance looks to Pidge for her opinion. She place she a hand on his shoulder to reassure him, and Lance takes this as a green light to go forward. This suggests that Lance values Pidge's opinion and trusts her judgement, since he sees her as the smart one of the team.

This whole time, however, Lance believed that Pidge was a boy. In reality, Pidge had disguised herself as a boy and snuck into the Garrison to get information on her missing family. When Pidge later reveals this information to the rest of Team Voltron, Lance is the only one who is surprised. He cries out in shock because he had no idea, but he doesn't treat Pidge any different than before.

Although Lance and Pidge haven't yet had any emotional one-on-one moments in the show, there have been several small scenes to show the growth of their friendship. Throughout the series, Lance and Pidge are shown working together and playfully teasingly each other several times. This includes Pidge zapping Lance with her bayard when he makes fun of its size, Pidge getting exasperated with Lance's constant flirting with pretty girls, Lance being unable to understand Pidge's love for technology and her scientific babble, Pidge and Lance bragging to each other twice (both times making Lance blush), the two of them combining their lions' powers to "stitch" a crumbling planet, nudging each other, gossiping with each other, and several other moments.

Despite their friendship being rocky at times, they obviously care about each other. When Pidge was attacked by Sendak and was held in his grasp, Lance sat up to shoot Sendak and save her, despite being heavily injured and essentially comatose. Pidge's later mimics this for Lance in the next season.

In the Space Mall, Pidge sees an Earth video game she wants to buy, and drags Lance with her to go get the money. The two then spend their time wading though the mall's fountain looking for change. Later, Lance is seen playing the game in his room, suggesting that the two may play video games together offscreen.

When Pidge was stranded alone on a trash nebula, she makes trash sculptures of all her friends. Later, Trash Lance is seen in Pidge's room.

Fanon
Plance started off as an obscure ship in the Voltron fandom, but gained a lot of traction after the second season. It now has a decently sized fanbase with many dedicated fans.

Shippers have speculated that Pidge may have a crush on Lance, similar to Toph's crush on Sokka in Avatar: The Last Airbender. Their evidence stems from the subtle differences in how Pidge treats Lance vs everyone else. Pidge got mad at Hunk for trying to touch her computer in the first episode, but Lance is often seen with things such as he really phone, headphones, and video game systems that she set up. Pidge has teased Hunk and Coran for having "girlfriends," but she gets annoyed when she notices Lance paying attention to pretty girls, suggesting jealousy.

Fans have also noticed that Lance appears to be staring in attentive confusion at the scientific things that Pidge is interested in. They have speculated that he's trying to understand her perspective. Similarly, a small picture of a sunset was spotted in Pidge's room after Lance mentioned that sunsets were pretty.

Fans also like to joke that Pidge and Lance are the adoptive parents of Kaltenecker, the cow they received at the Space Mall.

In most Plance works and theories, Pidge is thought to be a tsundere for Lance.