This paper assesses the applicability of new Keynesian DSGE models to a typical low income economy like those in Sub Saharan Africa. To this effect, we first review the development, criticisms and recent advances in DSGE modeling. Then we assess the implications of the assumptions of the standard open economy New Keynesian DSGE model within the context of the economic environment of a typical low income economy. Our assessment shows the following two points. First, though there are many criticisms to these models, most recent advances seem to have addressed most of these criticisms. However, there are still some outstanding criticisms that are serious challenges not only to DSGE models but also to all conventional economic models. Second, the current tendency of applying these models to explain or predict economic phenomenon in low income countries without incorporating the structural specificities of these countries cannot be justified. In stead, for these models to be helpful to understand the economic events in low income countries, most of their components must be changed or modified so that these models capture some salient specificities of low income economies. In this study we identify some of these components and suggest the possible changes or modifications.