The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: Any data service is in-stantly accessible everywhere. With each generation of cel-lular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by de-livering a WiFi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years [1], as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate require-ments specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological prepa-rations for 5G networks: higher peak rates, improved cover-age with uniform user experience, higher reliability and lower latency, better energy efficiency, lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the exis-tence and tradeoffs between multiple objectives. In this article, we provide a review of multi-objective opti-mization (MOO), which is a mathematical framework to solve design problems with multiple conflicting objectives [2–6]. In contrast to conventional heuristic approaches where some objectives are converted into constraints, MOO enables a rig-orous network design. MOO has been applied in many en-gineering and economic related fields, but has received little attention from the signal processing and wireless communi-cation communities. We provide a survey of the basic defini-tions, properties, and algorithmic tools in MOO. This reveals how signal processing algorithms are used to visualize the in-herent conflicts between 5G performance objectives, thereby allowing the network designer to understand the possible op-erating points and how to balance the objectives in an efficient and satisfactory way. For clarity, we provide a case study on massive multiple-input multiple-output (MIMO) systems, which is one of the key enablers of 5G cellular networks.