I will discuss two examples of cases where combining complementary cosmological probes is crucial for obtaining strong constraints on fundamental physics. First, I will present constraints from current data on neutrino mass and the number of neutrino species, when the primordial power spectrum (PPS) is not restricted to a power law form, but is instead left a free function. While CMB data alone (including the latest Planck data) measure the PPS to better than 10% for a large range of wave vectors (k=0.01-0.25 Mpc^-1), the effects of neutrino properties on the data are degenerate with those of the PPS so that neutrino mass and Neff bounds are weakened significantly when the PPS is left free. Strong neutrino constraints can be obtained regardless of the assumed PPS only when CMB data are combined with late-universe probes, such as galaxy clustering from BOSS. In the second part of this talk, I will discuss the complementarity between near-future weak lensing and galaxy clustering surveys such as SuMIRe (Subaru Measurements of Images and Redshifts), showing that the combination of these probes promises much tighter dark energy and modified gravity constraints than those from either probe alone.