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The success of the standard concordance cosmological model in predicting the primordial abundances of the light elements, and modeling the power spectrum of fluctuations of the cosmic microwave background have suggested to many that its ingredients are all one needs to understand galaxies and galaxy systems. However, a number of known problems with this expectation may signal the failure of standard gravity theory already on galaxy scales. An alternative nonrelativistic gravity theory - AQUAL, suggested by the phenomenological MOND paradigm, does rather well for galaxy scale systems, but performs poorly on cluster scales. I will discuss an improved AQUAL with potential for naturally handling clusters without addition of neutrinos or other nonbaryonic matter. Promoting AQUAL to a relativistic theory is not straightforward because of the constraints imposed by gravitational lensing. The obstacles were removed by TeVeS, historically the first covariant modified gravity theory consistent with MOND. After reviewing TeVeS's structure I will discuss its confrontation with gravitational lensing data. Time permitting I will overview work on the growth of cosmological fluctuations within TeVeS, and proposals to test this aspect of the theory with large galaxy and lensing surveys.

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