Networks constitute the backbone of many complex systems, on top of which collective behavior can emerge: from epileptic seizures in the human brain to the viral spread of rumours in a social network. When are simple network representations not enough? In this talk I introduce the topic of generalized networks, richer architectures which allow to consider the temporal and multiplex dimensions of relationships, and to go beyond simple pairwise interactions. Building on my contributions to the field, I focus on how to measure multiplexity in real-world systems from the micro to the macro scale, with examples from social, transportation and biological networks, and provide a short perspective on dynamical processes on generalized networks, searching for new emergent collective behavior and warning against overly optimistic statements associated to the multiplex nature of interactions.