Jet calculus: Resolving QCD jets in leading log approximation and beyond

We review recent developments in the study of hadronic jets produced in hard processes, based on perturbative QCD and, in particular, on jet calculus. The first part is a brief summary of what has been done in the leading log approximation, presented from a somewhat novel point of view. In the second part, we derive and discuss the parton-probabilistic algorithms. The results and implications of the calculation to the next-to-leading order are discussed at the end