This is a very complex situation that can be traced back to Belgian colonisation in the 19th century (or to 1482 when Diogo Cao, a Portuguese navigator landed there and made contact with the king of the Kongo). The current war is a result of the Rwandan genocide. As the Ugandan backed Tutsi dominated rebel army swept through Rwanda it caused an influx of Hutu civilians, along with the militia that carried out the murders, into the Congo. The Hutu power group that carried out the genocide ran many of the refugee camps. They used these camps as a base to launch further attacks on Tutsis and moderate Hutus across the border. Up to 20’000 people, many of them children, were killed in these attacks. UN inadvertently financed these attacks through its humanitarian aid programmes in the camps.
After numerous threats and one invasion (resulting in a massacre or at least hundreds) in one of the camps the Rwandans invaded again, this time with the Ugandan army. What started out as a war to stop murder quickly descended into a war for control of the Congo’s natural resources (The disc drive head in the reader head of your iPod is probably made from Titanium mined in the Congo). The Congolese rebels who overthrew Mobutu soon fragmented and with backing from Rwanda and Uganda some of them tried to overthrow Laurent Kabila, their new president. Troops from Namibia, Chad, Sudan, Angola and Zimbabwe were sent to support him. More importantly each of these countries backed different tribal groups. The resulting war caused utter chaos with Rwanda and Uganda finding themselves on different sides of the conflict.
Laurent Kabila was shot in 2000 (I think) and his less corrupt and despotic son took over. There is meant to be a South African backed ceasefire in place but it has been less than watertight. With so much money at stake and so many power brokers there is little chance of a clean break from the past. The influence of the USA and the French cannot be ignored either. The future is not bright.