Metal additive manufacturing has significantly evolved since the 1990s, achieving a market valuation of USD 6.36 billion in 2022, with an anticipated compound annual growth rate of 24.2% from 2023 to 2030. While powder-bed-based methods like powder bed fusion and binder jetting dominate the market due to their high accuracy and resolution, they face challenges such as lengthy build times, excessive costs, and safety concerns. Non-powder-bed-based techniques, including direct energy deposition, material extrusion, and sheet lamination, offer advantages such as larger build sizes and lower energy consumption but also encounter issues like residual stress and poor surface finish. The existing reviews of non-powder-bed-based metal additive manufacturing are restricted to one technical branch or one specific material. This survey investigates and analyzes each non-powder-bed-based technique in terms of its manufacturing method, materials, product quality, and summary for easy understanding and comparison. Innovative designs and research status are included.