In recent years, many physicists have used evolutionary game theory combined with a complex systems perspective in an attempt to understand social phenomena and challenges. Prominent among such phenomena is the issue of the emergence and sustainability of cooperation in a networked world of selfish or self-focused individuals. The vast majority of research done by physicists on these questions is theoretical, and is almost always posed in terms of agent-based models. Unfortunately, more often than not such models ignore a number of facts that are well established experimentally, and are thus rendered irrelevant to actual social applications. I here summarize some of the facts that any realistic model should incorporate and take into account, discuss important aspects underlying the relation between theory and experiments, and discuss future directions for research based on the available experimental knowledge. This work was partially supported by the EU through FET-Proactive Project DOLFINS (contract no. 640772) and FET-Open Project IBSEN (contract no. 662725), and by Ministerio de Economía y Competitividad (Spain)/FEDER (EU) grant VARIANCE (contract no. FIS2015-64349-P). Project IBSEN is in fact about large-scale experiments and provides a open-access platform for researchers to carry out them.