We described algorithms for computing the topology of real algebraic implicit curves and surfaces in dimension 3, based on projections techniques, starting with the algorithm for implicit planar curves. Then we consider curves in dimension 3. Next we describe an algorithm for computing the topology of a general real algebraic surface S. The approach is based on tools from stratification theory and the construction of an explicit Whitney stratification of S. We show how these methods can be turned into effective algorithms, using resultant ans subresultant computations and discussed the problem of iterated resultants and discriminants, for which we give some explicit formula.