Computing the topology of a geometric object defined implicitly appears in many geometric modeling problems, such as surface-surface intersection, self-intersection, arrangement computation problems ... It is a critical step in the analysis and approximation of (semi-)algebraic curves or surfaces, encountered in these geometric operations. Its difficulties are mainly due to the presence of singularities on these algebraic objects and to the analysis of the geometry near these singular points. The classical approach which has been developed for algebraic curves in the plane projects the problem onto a line, detects the value which are critical for this projection and lift points back on the curve at these critical values and in between. Information on the number of branches at these critical values or genericity condition tests on the number of critical points above a value of the projection have to be computed, in order to be able to perform correctly the combinatorial connection step of these algorithms. This approach has also been extended to curves and surfaces in 3D. In the talk, we will consider methods which requires information on the boundary of regions instead of information at critical points. We will describe a new method for computing the topology of planar implicit curves, which proceed by subdivision and which only requires the isolation of extremal points. Extension of this approach to curves and surfaces in 3D will be described. Experimentation of these algorithms based on the subdivision solvers of the library SYNAPS and the algebraic-geometric modeler AXEL will shortly demonstrated.