Additive Manufacturing (AM) has solidly established itself not only in rapid prototyping but also in industrial manufacturing. Its success is mainly determined by a possibility of manufacturing components with extremely complex shapes with minimal material waste. Rapid development of AM technologies includes processes using unique new materials, which in some cases is very hard or impossible to process any other way. Along with traditional industrial applications AM methods are becoming quite successful in biomedical applications, in particular in implant and special tools manufacturing. Here the capacity of AM technologies in producing components with complex geometric shapes is often brought to extreme. Certain issues today are preventing the AM methods taking its deserved place in medical and biomedical applications. Present work reports on the advances in further developing of AM technology, as well as in related post-processing, necessary to address the challenges presented by biomedical applications. Particular examples used are from Electron Beam Melting (EBM), one of the methods from the AM family.