Liverworts are flat growing green plants, closely related to mosses (Bryophytes). They have no stem and only a thallus, the flat leaf-like structure that is seen above ground. They belong to group called Hepatics and belong to the Marchantiophyta, a division of bryophyte plants, the mosses. These plants are primitive, not only in structure, but also in the fact that they are old. Some sources mention that they transition onto land during the Devonian Era (400 million years ago). Goes well with Bonsai then, I hear you say. Not really.
Bonsai growers will find these plants in moist areas. Where I live we have a high rainfall in winter and I have to be very careful with watering. This is usually taken care of by ensuring that the soil medium is free draining. Most of the liverworts that I see growing on soil come from nursery sourced plants, probably because the soil contains the spores and the fact there could be lot more organic soil in nursery plant soils.
The problem for me is that they can rapidly cover the surface of the soil and prevent water from penetrating the soil. This is not necessarily a problem as they already indicate that the soil is too wet. This layer of Liverwort can also prevent proper air circulation through the soil. I have also had experience of Liverwort growing over moss (I want the moss), suffocating the moss to death.
These plants reproduce asexually and sexually. They produce bumps (cupules) on the leaves, usually during late autumn, containing “eggs” called gemmae. These produce new plants. The sexual reproduction produces spores which germinate and form new plants.
As said, these plants can be an indicator that your soil or growing medium is too wet. If this is the case, it is obvious that the medium must be changed to be more free draining. Larger inorganic particles can be used to do this. If it is still a problem, look at the top layer of the soil. This could contain spores of liverwort. Scrape the top layer off and replace with a coarse material like gravel or pea metal.
Harsh chemicals could be used to spray on the liverwort to kill them off, but I have found that dabbing or brushing vinegar on the leaves of the liverwort, kills them off as well.
References:
Bonsaiplace 
Yep, Brushing with Malt Vinegar definitely works. It also works on unwanted moss on trunks where the bark needs to be protected and brushing isn’t possible. Some inevitably leeches into the growing medium but I have never noticed any side effects on the trees.
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