Artificial intelligence (AI) conversational agents (CA) or chatbots represent one of the technologies that can provide automated customer service for companies, a trend encountered in recent years. Chatbot use is beneficial for companies when associated with positive customer experience. The purpose of this paper is to analyze the overall customer experience with customer service chatbots in order to identify the main influencing factors for customer experience with customer service chatbots and to identify the resulting dimensions of customer experience (such as perceptions/attitudes and feelings and also responses and behaviors). The analysis uses the systematic literature review (SLR) method and includes a sample of 40 publications that present empirical studies. The results illustrate that the main influencing factors of customer experience with chatbots are grouped in three categories: chatbot-related, customer-related, and context-related factors, where the chatbot-related factors are further categorized in: functional features of chatbots, system features of chatbots and anthropomorphic features of chatbots. The multitude of factors of customer experience result in either positive or negative perceptions/attitudes and feelings of customers. At the same time, customers respond by manifesting their intentions and/or their behaviors towards either the technology itself (chatbot usage continuation and acceptance of chatbot recommendations) or towards the company (buying and recommending products). According to empirical studies, the most influential factors when using chatbots for customer service are response relevance and problem resolution, which usually result in positive customer satisfaction, increased probability for chatbots usage continuation, product purchases, and product recommendations.