When using polymer materials as scaffolds for tissue engineering or regenerative medicine applications the initial, and often lasting, interaction between cells and the material are via surfaces. Surface engineering is an important strategy in materials fabrication to control and tailor cell interactions whilst preserving desirable bulk materials properties. Surface engineering methods have been described that can strongly influence cell adhesion, migration, proliferation, differentiation and functionality. This review aims to categorise the current strategies for modifying surface chemistry and/or topography in terms of the resultant change in cell behaviour.