The personalized experience gets more and more attention these days. Many e-commerce businesses are looking for methods to deliver personalized service. Consumers are expecting, if not demanding, highly personalized experiences. Moreover, customers are typically willing to spend more when they receive such a custom-tailored service. A prerequisite to provide a genuinely personalized experience is to understand the customer. Intent detection is a new and challenging approach in modern e-commerce to understand the customer. We find that various aspects of customer intent detection can be tackled by leveraging tremendous recent recommendation systems' progress. In this work, we review existing works from different domains that can be re-used for customer intent detection in the e-commerce. Even though many methods are used, there is no comparison of available approaches. Based on a review of nearly 100 articles from 2015 until 2019, we propose a categorization of types of intent detection, personalization context, building a customer profile, and dynamic changes in user interests handling. We also summarize existing methods from applicability in the e-commerce domain, including the aspect of the General Data Protection Regulation requirements. The paper aims at the classification of applied techniques and highlights their advantages and disadvantages.