Laser Additive Manufacturing (LAM) of parts and components fascinates due to process specific advantages such as nearly unrestricted geometrical freedom, material freedom and achievable properties of the parts built-up. Hence, adaptive parts and components can be manufactured, repaired and modified by LAM. This article presents the advances in speeding up the LAM techniques Selective Laser Melting (SLM) and Laser Metal Deposition (LMD) towards higher speeds and deposition rates. In the first part build up increase for (SLM) is presented. The main approach for higher build up rates is the use of higher laser power up to 1kW. A machine concept and process strategies for the efficient transfer of laser power into build up rate for different materials (aluminum ans steel) will be presented. The second part focuses on investigations on LMD at high processing speeds of up to 600 m/min. Process basics and achieved results in terms of layers are presented. This new process enables to produce dense layers with thicknesses ranging from 10 μm up to 0.3 mm in one pass with very low dilution at high speeds, resulting in completely new advantages regarding economic efficiency of LMD processes.