We describe the Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X), a probeclass mission concept that will provide an unprecedented view of the X-ray sky, performing timing and spectroscopy over both a broad energy band (0.2–30 keV) and a wide range of timescales from microseconds to years. STROBE-X comprises two narrow-field instruments and a wide field monitor. The soft or low-energy band (0.2–12 keV) is covered by an array of lightweight optics (3-m focal length) that concentrate incident photons onto small solid-state detectors with CCD-level (85–175 eV) energy resolution, 100 ns time resolution, and low background rates. This technology has been fully developed for NICER and will be scaled up to take advantage of the longer focal length of STROBE-X. The higher-energy band (2–30 keV) is covered by large-area, collimated silicon drift detectors that were developed for the European LOFT mission concept. Each instrument will provide an order of magnitude improvement in effective area over its predecessor (NICER in the soft band and RXTE in the hard band). Finally, STROBE-X offers a sensitive wide-field monitor (WFM), both to act as a trigger for pointed observations of X-ray transients and also to provide high duty-cycle, high time-resolution, and high spectral-resolution monitoring of the variable X-ray sky. The WFM will boast approximately 20 times the sensitivity of the RXTE All-Sky Monitor, enabling multi-wavelength and multi-messenger investigations with a large instantaneous field of view. This mission concept will be presented to the 2020 Decadal Survey for consideration.