Advancing from two core traits of biological systems: multilevel network organization and nonlinearity, we review a host of novel and readily available techniques to explore and analyze their complex dynamic behavior within the framework of experimental-computational synergy. In the context of concrete biological examples, analytical methods such as wavelet, power spectra, and metabolomics-fluxomics analyses, are presented, discussed, and their strengths and limitations highlighted. Further shown is how time series from stationary and nonstationary biological variables and signals, such as membrane potential, high-throughput metabolomics, O₂ and CO₂ levels, bird locomotion, at the molecular, (sub)cellular, tissue, and whole organ and animal levels, can reveal important information on the properties of the underlying biological networks. Systems biology-inspired computational methods start to pave the way for addressing the integrated functional dynamics of metabolic, organelle and organ networks. As our capacity to unravel the control and regulatory properties of these networks and their dynamics under normal or pathological conditions broadens, so is our ability to address endogenous rhythms and clocks to improve health-span in human aging, and to manage complex metabolic disorders, neurodegeneration, and cancer. WIREs Syst Biol Med 2017, 9:e1352. doi: 10.1002/wsbm.1352 For further resources related to this article, please visit the WIREs website.