Tissue engineering, an area of intense interest from academic, clinical, and commercial perspectives, involves regrowing tissue and/or organs using biological materials most commonly obtained from the patient or from a donor. In most cases, successful tissue engineering requires the use of a scaffold to guide the formation of the new tissue. This work reviews some of the common methods used to prepare polymeric scaffolds for tissue engineering and, more broadly, for the culture of cells in 3D. Scaffolds require, amongst other parameters, an interconnected network of holes (pores) to allow cells to grow into the materials, and to provide effective nutrient access and waste removal. The use of fabrication methods including electrospinning, thermally induced phase separation, emulsion templating and the so-called 'breath figure' approach, to achieve such an interconnected pore network is discussed. Each method is described in some detail and examples of polymers that can be used with each one are given. The use of additives to improve the physical/mechanical properties of the scaffolds and to enhance their biological response is also discussed. In each case, examples of the use of each scaffold type in tissue engineering applications are presented.