Business processes are at the heart of each organisation by describing its way of working. Globalisation, higher competitiveness, more demanding customers, growing IT possibilities, etc.; all those challenges put pressure on organisations to perform better, and thus to obtain mature (or excellent) business processes. Consequently, business process maturity models (BPMMs) have been designed to help organisations gradually assess and improve their business processes. Some well-known examples are CMMI or OMG-BPMM, but many others exist. In fact, so many BPMMs are around these days that organisations cannot see the wood for the trees. They risk selecting a BPMM that does not fit their needs, or a BPMM that might be of lower quality. Moreover, academics have frequently criticised maturity models for being consultancy speech, as those models typically simplify the complex reality. This criticism is primarily explained by the limited scientific knowledge on business process maturity, and how to measure and improve it. Particularly, we encountered three open knowledge issue: (1) scarce literature on BPMMs (indicating an unexplored research domain), (2) no comprehensive comparative studies on BPMMs (in contrast to the huge number of existing BPMMs), and (3) no theories on business process maturity (in contrast to the criticism). Nevertheless, the essential process improvements are not easy to realise and organisations may need some practical guidance on their journey towards excellence. Consequently, BPMMs remain important tools to help organisations, but they must be thoroughly examined to allow a critical view on the many BPMMs and to theoretically underpin them. For this purpose, the dissertation provides a comprehensive overview of existing BPMMs (N=69). By including non-academic BPMMs, our sample is more comprehensive than other BPMM overviews. Further on, by including different process types (i.e. generic business processes, supply chains, and collaboration processes), our sample suggests versatility which should facilitate transferability of our findings to other process types. To properly investigate the problem statement, this dissertation covers three studies: 1)a literature study to define the main concepts related to BPMMs, in order to obtain a common understanding to start from (issue 1 and 2). It elaborates on the differences between a business process, process management and process orientation, and on the differences between maturity and capability. A resulting BPMM definition is provided in a textual description, as well as in a conceptual model; 2)a classification study to identify and organise the possible capability areas and maturity types of BPMMs, in order to strengthen the BPMM foundation (issue 1, 2 and 3). Based on cluster analysis and discriminant analysis, different types of maturity were identified in the BPMM sample. Therefore, the 69 BPMMs were mapped to theoretical main capability areas and sub areas, supplemented by their number of business processes addressed; 3)a selection study to identify the criteria to be considered when choosing a BPMM out of the wide array, in order to derive evaluation scores for BPMMs and to provide practical advice on BPMM selection (issue 1 and 2). An international Delphi study was conducted to identify and weigh the most important selection criteria, and to evaluate the sampled BPMMs accordingly. The final selection advice is bundled in a free and online decision tool, called the BPMM Smart-Selector.