Introduced to Europe by well-meaning botanists in the 19th Century and enjoyed for its bamboo-like qualities and ability to grow anywhere, it has since become a menace. Rapid-growing and with no natural predators, it's powers of propagation and the damage it can cause to infrastructure, buildings and their foundations means that it's now illegal to plant it or cause it to grow in the wild.
Successful removal is extremely expensive. It necessitates the control of its above-ground foliage over several years with the correct herbicide and the total eradication of its below-ground root network. Companies who specialise in its removal will excavate one metre around the extensive root structure of the knotweed. The excavated earth, designated as controlled waste under the Environmental Protection Act, must then be disposed of properly. It is usually incinerated.
Press attention of knotweed has centred around mortgage lenders' restrictive lending policies until recently a mortgage lender would not lend on a property affected by knotweed or in the vicinity of it. Rules have been relaxed slightly but it still can cause a major issue with funding. Removal of a large patch on the London Olympic site cost millions and DEFRA estimates the cost of its total eradication from the UK to be 1.56 billion.
In a recent County Court case, Williams v Network Rail Infrastructure Ltd  UK CC, two homeowners brought a private nuisance claim against Network Rail. Their homes were next to a railway embankment owned by Network Rail that was infested with knotweed which persistently spread to the homeowners' land.
Interestingly, the homeowners' claim for nuisance based on the fact that the knotweed had encroached onto their land failed, as the knotweed had not yet caused any physical damage to their properties.
However, their claim for nuisance based on its presence on the homeowners' land succeeded and they were awarded damages for treatment costs, the diminution in value of their homes (the reduced value after treatment, to reflect the stigma attached to the properties) and general damages for loss of amenity and interference with quiet enjoyment. The court decided that Network Rail had constructive knowledge of the risk of both the spread of knotweed and consequential damage to the properties (since the publication of RICS knotweed guidance in 2012-13) and that it had failed to tackle the problem and as such Network Rail had failed to prevent interference with quiet enjoyment of the homeowners' land.
The clear message being that if a landowner is aware of knotweed on their land and that it has spread or has the potential to spread, there is a risk of a private nuisance claim being brought even though the knotweed hasn't (yet) caused any physical damage.