Logistics processes allow for the movement of goods along the supply chain to the customers. Companies are using digital solutions more widely to support their logistics processes. Current studies focus mainly on the intrinsic perspective of the digital maturity of logistics processes. Rarely do previous studies consider the impact of external factors (e.g., market trends, as external drivers at the strategic level) on the digital maturity of logistics processes. In this paper, our aim is to propose a novel generic approach to measuring the level of adoption of digital technologies in logistics processes. We applied the maturity model theory to provide a generic framework for the assessment of different partners in supply chains (suppliers, manufacturers, retailers, e-tailers, logistics service providers) in a homogeneous way. We propose the five levels (Avoiding, Discovering, Adopting, Improving, Excelling) to measure the frequency of the application of the digital technologies with high intelligence in the domain of logistics processes. Furthermore, we investigate the relationship between the selected market trends, which are external drivers at the strategic level, and the digital maturity of logics processes. We conducted the survey among a group of 38 companies to classify their maturity level and then to test which market trends motivate them to digitalize their processes. We applied Bayesian statistics to test the level of the relationship between the digitalization of logistics processes and four market trends, namely, the sustainability, e-commerce, sharing economy, and speed-orientation of customers. The results show that all the trends tested moderately and positively influence the digital maturity of logistics processes.