The arc welding process is widely used in industry, but the automatic control is limited by the difficulty in the process for measuring the principal magnitudes and to close the control loop. Adverse environmental conditions make use of conventional measurement systems difficult for obtaining information of the weld bead geometry. Under these conditions, indirect sensing techniques are a good option. Different sensing and estimation techniques are used, but few researchers are focusing on the flat welding position. The theory and practice prove that the dynamic models are the best representation to control the welding process, but most studies are performed with static models. This work is a review of the algorithms and sensing techniques used for collecting values of the arc welding process that allow the measurement or estimation of the weld bead geometry. Special attention is given to sensor fusion techniques due to its promising future in the welding process. Discussed in this text are the papers, patents, thesis and other documents found on the theme. It shows a summary of their evolution over the last 50 years.