Climate change is causing sea level to rise
In theory, rising global temperatures should cause average sea level to rise for two main reasons. First, water expands as it warms. Second, warming temperatures should make glaciers and ice sheets export ice to the ocean faster — by melting faster, and, for tidewater glaciers, by flowing faster and depositing more icebergs into the sea.
Many lines of evidence bear out the theory. Sea level has already been rising over the last century in concert with warming air and ocean temperatures, plus the shrinking of glaciers and ice sheets.[[Bindoff, N.L., J. Willebrand, V. Artale, A, Cazenave, J. Gregory, S. Gulev, K. Hanawa, C. Le Quéré, S. Levitus, Y. Nojiri, C.K. Shum, L.D. Talley and A. Unnikrishnan, 2007: Observations: Oceanic Climate Change and Sea Level. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.]] It is even the case that regions where the ocean has warmed more have seen faster sea level rise (from the expanding, warming water) .[[Cazenave, A., and R. S. Nerem. “Present-day sea level change: Observations and causes.” (Abstract) Reviews of Geophysics 42 (2004).]]
Furthermore, studies of ancient climate indicate that sea level was much lower than today during colder periods[[For example, see: Clark, P. U. and A. C. Mix. “Ice sheets and sea level of the Last Glacial Maximum.” (PDF) Quaternary Science Reviews 21 (2002): 1-7.]], and much higher during warmer ones.[[For example, see: Rohling, E. J., K. Grant, C. H. Hemleben, M. Siddall, B. A. A. Hoogakker, M. Bolshaw, and M. Kucera. “High rates of sea-level rise during the last interglacial period.” (Abstract) Nature Geoscience 1 (2007): 38-42.]]