ABSTRACT We present the results of the Swift and NuSTAR observations of the nearby BL Lac object Mrk 421 during 2013 January-June. The source exhibited a strong long-term variability in the 0.3-10 keV and 3-79 keV bands with the maximum-to-minimum daily-binned flux ratios of 22 and 95, respectively, in about 3 months, mainly due to unprecedented strong X-ray outbursts by more than an order of magnitude in both bands within 2 weeks in 2013 April when the 0.3-10 keV count rate exceeded the level of 200 cts s−1 for the first time, and Mrk 421 became one of the brightest sources in the X-ray sky. The source was also very active on intra-day timescales, and it showed flux doubling and halving timescales of 1.16-7.20 hr and 1.04-3.54 hr, respectively. On some occasions, the flux varied by 4%-23% within 300-840 s. During this period, the source also exhibited some of the most extreme X-ray spectral variability ever reported for BL Lacs-the location of the synchrotron spectral energy distribution peak shifted from a few eV to ∼10 keV, and the photon index at 1 keV and curvature parameter varied on timescales from a few weeks down to intervals shorter than 1 ks. MAGIC and First G-APD Cherenkov Telescope observations also revealed a very strong very high energy (VHE) flare during April 11-17. The UV and HE γ-ray flares were much weaker compared to their X-ray counterparts, and they generally showed significantly stronger correlation with each other than with the X-ray fluxes.