The emphasis on point-like source searches for astrophysical neutrinos has recently been strengthened by the unambiguous detection of high-energy astrophysical neutrinos by IceCube. So far, the limited statistics and angular resolution of the relevant analyses do not resolve more than an isotropic emission of astrophysical neutrinos. We present the results of searches for neutrino emission of point-like sources using six years of integrated IceCube livetime, of which three years use the complete IceCube detector. Focusing on track-like events induced by chargedcurrent muon-neutrinos, a large statistics sample of ∼ 600 000 events on the full sky with median angular resolution between 1 • and 0.4 • , improving with higher energy, has been collected. For the southern hemisphere, the main background consists of bundles of muons created in extensive air-showers in the Earth's atmosphere, whereas the northern hemisphere is dominated by neutrinos created in the same process. Using an unbinned likelihood maximization search for local clustering, IceCube is sensitive to sources in the northern sky with fluxes substantially below E 2 ∂ φ / ∂ E = 10 −12 TeV cm −2 s −1 . We report about the status of these searches and the implications on the nature of the observed flux as well as on single source candidates.