The plague comes in three forms. Bubonic plague (the most famous) is the infection of the lymphatic system, septicemic plague is infection of the blood and pneumonic plague is the infection of the lungs. Bubonic plague requires you to come in to contact with an infected person or animal. Pneumonic plague can be spread through bodily fluids, or even through the air.
It's enough to cause panic, which explains why the Chinese government initially tried to cover the incidents up. The diagnoses were made on November 3, but it wasn't until November 13 that the government reported the incident to the World Health Organisation (WHO), as required. Before then, the Chinese media had got a hold of the story and the government was doing everything they could to censor details online.
Should we be concerned about this? It's unlikely. Geneticists have been studying the bacteria for a long time. They've been trying to predict how it will evolve, so they can be ready for it, if it tries to make a serious comeback. Current strains of the infection can easily be treated by antibiotics, as long as it's caught early on.
In 2014, David Wagner from North Arizona University told the BBC: "Plague strains are always emerging from rodent reservoirs, causing disease in humans, but what we don't see are the widespread pandemics because now the public health response would be quick and very concentrated to shut that down."
The plague isn't back. It never really left. In 2014, there were 16 reported cases of the plague. Between 2010 and 2015, the plague was responsible for 584 global deaths - mostly in poorer areas of Africa, Asia and South America where the infrastructure and availability of antibiotics is restricted. Compared to malaria, which kills hundreds of thousands every year - the plague does not seem like something we should lose sleep over.