The recent discovery of the accelerated cosmic expansion suggests that our Universe may be endowed with a positive cosmological constant Λ. In addition, even though general relativity (GR) is a very successful and well-tested theory, it could be that it is not the final theory of gravity. Brans-Dicke theory is one of the first and simplest modifications of Einstein’s theory. During this talk, I will present the study of cosmic structures in Brans-Dicke-like theories in the presence of a positive cosmological constant. I will discuss the validity of the no-hair theorem in the context of such theories. Moreover, I will show that, the black hole solutions in these theories are no different from those in GR and also that the presence of a stationary cosmological event horizon rules out any regular spherical stationary solution, appropriate for the description of a star.