We propose a Key Project to investigate transient dimming of young stars by occulting circumstellar dust. Dimming can be up to several tens of percent and is detectable from the ground, but the diversity of this phenomenon has only been recently revealed by Kepler/K2. These stars, colloquially and collectively termed ``dipper'' stars, usually host circumstellar disks, and our investigation will probe of the structure, dynamics, and composition of material in the inner regions (<1 AU) of these disks in the range of separations where planets are found around older stars. Our studies will complement observations by interferometers such as ALMA, which cannot resolve the inner disks of stars even in the nearest star-forming regions. Occulting dust could be from asymmetric accretion onto the star, vertical structures produced by instabilities in highly inclined inner disks, clumpy dusty disk winds, gravitationally-bound planetesimal swarms, or evaporating planetesimals or ``exocomets''. The objectives of our Key Project are to determine the relative importance of each of these scenarios, detect any correlation with the properties of the stars and the evolutionary state of their disks, and obtain information about the composition of material that could be the building blocks of, or debris from planets. We will use LCO telescopes and obtain time-series photometry and spectroscopy of dimming events to achieve these objectives, i.e. by measuring the grain-size distribution of the dust, detecting any gas or volatilized elements associated with dust clouds, constraining the inclination of the motion of clouds with respect to stellar equators, and inferring the presence of massive sources on Keplerian orbits as potential sources of dust. Our Key Project will be organized into four campaigns: (1) multi-band monitoring of an ensemble of dipper stars, (2) triggered observations of individual dimming events using alerts from the Zwicky Transient Facility, Gaia, and the All-Sky Automated Survey for Supernovae; (3) time-critical observations of predicted quasi-periodic dimming events; and (4) observations with non-LCO telescopes to characterize the stars and disks studied by the other three campaigns. Our project exploits the unparalleled characteristics of the LCO telescope network: global longitudinal coverage to achieve near-continuous monitoring; access to the entire sky to study all of the nearest star-forming regions and young moving groups; automated, triggered scheduling of observations to study dimming events as they happen; and the NRES spectrograph network to make continuous measurements of the predicted Rossiter-McLaughlin effect due to the partial occultation of rapidly rotating young stars by dust. We have already obtained preliminary data demonstrating the feasibility of some parts of this project. Observations will be organized and scheduled using a Telescope Observing Management Systems (TOMS) that we will develop using the LCO TOMS Toolkit. Our international team is well positioned to conduct this project, with significant experience with the LCO telescope network, access to substantial non-LCO observing resources in both hemispheres to conduct necessary follow-up observations, and critical theoretical expertise to interpret these data and shed light on this mysterious phenomenon.