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tokens: We thank NuSTAR PI Fiona Harrison and Belinda Wilkes for granting NuSTAR and Chandra DDT observations of SGR J1935+2154 during the 2015 and 2016 outbursts, respectively. We also thank the Swift team for performing the monitoring of the source during all of its outbursts. G.Y. and C.K. acknowledge support by NASA through grant NNH07ZDA001-GLAST. A.J. and J.W.T.H. acknowledge funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013) ERC grant agreement no. 337062 (DRAGNET). The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968) and in alliance with Ana G. Méndez-Universidad Metropolitana and the Universities Space Research Association. We would like to thank Arecibo observatory scheduler Hector Hernandez for the support during our observations. A.J. thanks Daniele Michilli for helping with the single-pulse search analysis. We thank the anonymous referee for their careful reading and insightful comments that improved the quality of the manuscript. Software: CIAO ( http://cxc.harvard.edu/ciao/ ), SAS (v14.0.0, https://www.cosmos.esa.int/web/xmmnewton/sas ), xrtpipeline (v13.2), nustardas (v1.5.1, https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/ ), HEASOFT (v6.20, https://heasarc.nasa.gov/lheasoft/ ), ChaRT ( http://cxc.harvard.edu/ciao/PSFs/chart2/ ) MARX ( http://space.mit.edu/CXC/MARX/ ), PRESTO (Ransom 2001 ; Ransom et al. 2002 , 2003 ), XSPEC (v12.9.0k; Arnaud 1996 ).