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Hakurei Border (Hakurei Dai-Kekkai, lit. Hakurei Great Border, 博麗大結界) is the border between Gensokyo and the outside world. This was created in Meiji 17 (AD 1884), the creation of which marks year 0 on Gensokyo's Timeline. It's often refered to as the "Border," "Hakurei Barrier," "Great Boundary," etc. It is known that the Hakurei Shrine is located on the border and believed that Yukari Yakumo lives somewhere along the border as well (though not near the shrine).
It is the strongest boundary in all of Gensokyo, with Youkai reinforcing the original work done by humans in 1884. Yuyuko has speculated that not even Yukari could make a boundary of this level (from scratch, on her own). Yet it is not completely impenetrable. Examples of this include various individual people (Reisen, Chiyuri, Yumemi, Maribel, Sanae, Kanako, Suwako, and many others) that have arrived through it as well as entire locations (Moriya Shrine, Poltergeist Mansion, Scarlet Devil Mansion) that have been transported through the barrier.
The Hakurei Shrine is supposed to be the one gate through the boundary - this Shinto shrine exists on both sides of the border. Thus a lot of random items slip through and are found at the Shrine. Furthermore, people sometimes wander through the boundary and are either turned back with an illusion or they insist upon staying (in which case they're put in the Human Village for safety). However, Youkai teams sometimes go out to gather humans for cooking (a delicacy to them), hiding their activities with magic (lost people, accidents, etc). It's unlikely that Reimu (effectively the guardian of the gate) would endorse such actions so presumably Youkai know of ways to make a 'hole' in the border elsewhere - they originally helped reinforce it after all. Possibly all those 'border penetrations' that these cooking teams require are organized by Yukari, but this may not be necessary considering how many people and locations have come across the border on their own without her help.