Since their discovery in the early 1960s, Josephson junctions (JJs) remain at the forefront of advancing technology in superconducting electronics, sensing, high-frequency devices, and quantum science. An important JJ-based device is the superconducting quantum interference device (SQUID), a highly sensitive magnetometer that uses JJs to measure extremely small magnetic fields. From a dynamical point of view, the SQUID is a highly nonlinear system exhibiting extreme multistablity and chaos. In the first part of my presentation, I will talk about the complex dynamics of SQUID oligomers and metamaterials, i. e. artificially structured media of periodically arranged, weakly coupled elements, which show extraordinary electromagnetic properties and tunability. Another fascinating application of JJs involves their exploration for the design of superconducting neuromorphic computing systems. When combined in circuits, coupled JJs can emulate sophisticated properties found in biological neurons. From a technological point of view, JJ-based neuromorphic systems are particularly appealing due to their capacity to operate in great speeds and with low energy. In the second part of my talk I will present recent work on such JJ-based systems and discuss the mechanisms underlying the exhibited dynamical properties relevant for neurocomputation.