The survey discusses a new approach to Integer Programming which is based on the structural characterization of problems using methods of additive number theory. This structural characterization allows one to design algorithms which are applicable in a narrower, yet still wide, domain of problems, and substantially improve the time boundary of existing algorithms. The new algorithms are polynomial for the of problems in which they are applicable, and even linear ($O(m)$) for a wide of the Subset-Sum and Value-Independent Knapsack problems. Previously known polynomial time algorithms for the same es of problems are at least two orders of magnitude slower.