Open-domain chatbots that can engage in a conversation on any topic received significant attention in the last several years, which opened opportunities for studying user interaction with them. Drawing from reviews of chatbots posted on Google Play, we explore user experience and expectations of these agents in a mixed-method study. Results of statistical analysis reveal which social qualities of chatbots are the most significant for user satisfaction. Further, we employ natural language processing and qualitative methods to identify how users wish their chatbots to evolve in the future. While currently users mostly value the entertaining component of their experience, their expectations call for more human-like behavior of chatbots. The most prominent expectations include chatbots' abilities to treat and express emotions and be more attentive to the user. Based on these findings, we conclude with design implications, discussing the directions for developing social skills of open-domain chatbots.