The article considers a rapid development of digital technologies as one of the modern challenges for business. First of all, digital technologies affect communication between the company and its customers. Communications are established both by traditional and online means, so we can observe multi-channel communication. This is caused by the growing number of customers using mobile Internet. As a result, we see a significant change in customers’ expectations: they wish to get full information on the company, product, delivery conditions, e.g., on the value offered, at any time and with any device. That leads to the fact that all company’s activities are organized around the customers’ requests, which demonstrates the customer-centric approach to company management. The article investigates the specifics of a customer-centric company. Evolution of the customer-centric approach in the digital economy is considered. Contemporary problems of creating a customer-centric company caused by development of digital technologies and customers’ needs are analyzed. The specificity of digitalization as a condition for developing the customer-centric approach is classified. We have demonstrated strategic CRM to be an important characteristic of a customer-centric company. We have also revealed that in the digital economy, the term ‘client’ is broader than the term ‘customer’: both internal and external stakeholders can be regarded as clients. Impact of the customer-centric approach on BPM is shown. That means that the customers’ information should be used not only by front office units, but also by the other company’s departments. This requires complex business process transformation, from creating integrated information system to changing human resource management and corporate culture. We propose the architecture for further developing the topic on the analysis of business process transformation in the digital economy.