this paper we consider bundle methods under the light of inexact proximal point algorithms, namely the hybrid variant of [36], see also [35,37,38]. The insight given by this new interpretation is twofold. First, it provides an alternative convergence proof, which is technically simple, for serious steps of bundle methods by invoking the corresponding results for hybrid proximal point methods. Second, relating the two methodologies supplies a computationally realistic implementation of hybrid proximal point methods for the most general case, i.e., when the operator may not have any special structure. Our paper is organized as follows. In x 2 we outline the hybrid proximal point algorithm, together with its relevant convergence properties. Some useful theory from [9] and [8] on certain enlargements of maximal monotone operators is reviewed in x 3. Finally, in Section 4 we establish the connection between bundle and hybrid proximal methods and give some new convergence results, including the linear rate of convergence for bundle methods.