This paper introduces the recent theory of plausible and paradoxical reasoning, known as DSmT (Dezert-Smarandache Theory) in the literature, which deals with imprecise, uncertain and potentially highly conflicting sources of information. Recent publications have shown the interest and the potential ability of DSmT to solve fusion problems where Dempster-Shafer Theory (DST) provides counter-intuitive results, especially when conflict between sources becomes high and information becomes vague and imprecise. This short paper presents the foundations of DSmT, its main rules of combination including the most recent ones and introduce briefly some open challenging problems in fusion.