Using visual, photographic, and photoelectric measurements, we have constructed a historical light curve for the young binary system UY Aur on an interval longer than 100 yr. About a quarter of all magnitude estimates have been obtained for the first time from photographic plates of the Sternberg Astronomical Institute and Harvard College Observatory Astronomical Plate Stacks. Analysis of the light curve and the magnitude dependences of the polarization and color has led us to the following conclusions. Cyclic variations in the seasonally mean brightness of the binary’s primary component UY Aur A with a period of ≃16.3 yr occurred from the mid-1920s to the mid-1940s and after 1986. The variations are caused by the change in the rate of disk accretion onto the star attributable to the motion of the hypothetical companion UY Aur C around the primary star in an orbit with a semimajor axis of ≃ 6 AU. From the early 1950s to the mid-1980s, the periodicity of the seasonally mean variations was not noticeable due to nonperiodic eclipses of UY Aur A by gas-dust clouds. Between 1945 and 1974, another gas-dust cloud obscured and still obscures the component UY Aur B, causing its mean optical brightness to drop by several magnitudes. The role of the clouds that caused an almost simultaneous eclipse of the stars, whose separation in projection onto the celestial sphere exceeds 100 AU, is played by the denser and puffed-up regions of their accretion disks. These regions are the result of a dynamical interaction between the binary’s stars and the outer circumbinary accretion disk. The extinction variations with time are attributable to orbital motion of the binary’s stars and azimuthal inhomogeneity of the clump regions in the disks. A number of observational tests are suggested to verify our conclusions.