Business processes are basic enablers in sustaining an organization's existence in delivering high-quality products and services. A maturity model is an instrument to assess and continually improve business processes. For example, Capability Maturity Model Integration for Development (CMMI-Dev) in software domain has been used to assess and improve software processes in thousands of organizations worldwide since 1990s. Inspired by CMMI in the last decade, researchers and practitioners have proposed generic maturity models for business processes with varied focus and depth. However, the use of these models has not gained widespread acceptance in the Business Process Management (BPM) field. One of the reasons is the lack of a clear distinction between a maturity model and its assessment model. The objective of this study is twofold: First, to discuss challenges of business process assessment with regard to generic maturity models reported in scientific literature, and second, to identify key characteristics of a business process assessment model that would facilitate the use of maturity models in the BPM field.