To manage a growing number of users and an ever-increasing demand for bandwidth, future 5th Generation (5G) cellular networks will combine different radio access technologies (cellular, satellite, and WiFi, among others) and different types of equipment (pico-cells, femto-cells, small-cells, macro-cells, etc.). Multi-connectivity is an emerging paradigm aiming to leverage this heterogeneous architecture. To achieve this, multi-connectivity proposes to enable UE to simultaneously use component carriers from different and heterogeneous network nodes: base stations, WiFi access points, etc. This could offer many benefits in terms of quality of service, energy efficiency, fairness, mobility, and spectrum and interference management. Therefore, this survey aims to present an overview of multi-connectivity in 5G networks and beyond. To do so, a comprehensive review of existing standards and enabling technologies is proposed. Then, a taxonomy is defined to classify the different elements characterizing multi-connectivity in 5G and future networks. Thereafter, existing research works using multi-connectivity to improve the quality of service, energy efficiency, fairness, mobility management, and spectrum and interference management are analyzed and compared. In addition, lessons common to these different contexts are presented. Finally, open challenges for multi-connectivity in 5G networks and beyond are discussed.