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Strong fluctuations impacting open systems may induce tipping and system-wide cascading failure, yet it remains unclear under which conditions, how, and at which point fluctuation-driven systems tip. Here we report theoretical and methodological progress about tipping and its precursors in a range of externally driven nonlinear networked systems, substantially generalizing and going beyond work on one- and two-dimensional systems [1,2]. We combine self-consistency conditions, insights from periodically driven systems in electrodynamics and tools from harmonic balance and asymptotic analysis to uncover generic routes to tipping, to predict intrinsically nonlinear response dynamics before tipping and estimate the tipping point semi-analytically. We highlight several application directions and a broad range of unsolved questions.