In accordance with the present invention, there is disclosed surgical methods and apparatus for accessing and stabilizing the heart. The methods and apparatus facilitate access to an anastomosis site, allows various instruments or devices to be maneuvered and secured in place, and provide stabilization of the heart. The apparatus may involve a tissue stabilizer, and in particular a tissue stabilizer for use in immobilizing or stabilizing a portion of the beating heart using a compressive force delivered to the heart via the tissue stabilizer. The stabilizer may include a stabilizer base and a shaft. The shaft may be secured within an appropriate instrument mount preferably fixed to a retractor or other stable platform as disclosed herein. The stabilizers of the present invention provide improved access to a surgical site at a target vessel on the surface of the heart and may include features which facilitate optimal presentation of the target vessel.