The mechanical behavior of living cells is studied with micropipette suction in which the surface of a cell is aspirated into a small glass tube while tracking the leading edge of its surface. Such edges can be tracked in a light microscope to an accuracy of +/-25 nm and suction pressures as small as 0.1-0.2 pN/microm2 can be imposed on the cell. Both soft cells, such as neutrophils and red cells, and more rigid cells, such as chondrocytes and endothelial cells, are studied with this technique. Interpretation of the measurements with basic continuum models leads to values for a cell's elastic and viscous properties. In particular, neutrophils are found to behave as a liquid drop with a cortical (surface) tension of about 30 pN/microm and a viscosity on the order of 100 Pa s. On the other hand, chondrocytes and endothelial cells behave as solids with an elastic modulus of the order of 500 pN/microm2 (0.5 kPa).