The gravitational lensing constraints on the small mass end of the $\Lambda$CDM mass function are discussed. Here a conservative approach is taken where the most difficult to explain image flux anomalies in strong lenses are emphasized. Numerical simulations are performed to compare predictions for the $\Lambda$CDM small scale mass function with the observed flux ratios. It is found that the cusp caustic lens anomalies and the disagreements between monochromatic flux ratios and simple lens models can be explained without any substructure in the primary lenses' dark matter halos. Extragalactic $\Lambda$CDM halos are enough to naturally explain these cases. This does not mean that substructure within the host lens is not contributing. In fact, it could be dominating the lensing. It should also be noted that this extragalactic population has not been directly observed either.

Spectroscopic gravitational lensing provides more information on the nature of these substructures. In the one relevant case in which this technique has been used so far, observations of Q2237+0305, there is evidence that there are more small mass halos ($\sim 10^6\msun$) than is expected in the $\Lambda$CDM model.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html