The identification of the Black Death with plague is now fairly well-established - see this paper (open access) in which PCR and protein detection were used to detect the presence of _Yersina pestis_ in human skeletons from plague-related mass graves across Europe.
Outbreaks of plague do occur in rural environments, see this WHO page for some details. The WHO plays a role in responding to these outbreaks, as long as they are notified by the relevant countries. Plague infections respond well to antibiotic treatment.
There has also been a recent outbreak in Madagascar. According to the epidemiologists we are still in the midst of the 3rd plague pandemic, which started in China in the mid 19th century.