The application of synthesis of Petri nets from languages for practical problems has recently attracted increasing attention. However, the classical synthesis problems are often not appropriate in realistic settings, because usually it is not asked for plain-vanilla Petri net synthesis, but specific additional requirements have to be considered. Practitioners in industry are in need of a library of proper adaptations of the standard synthesis methods offering solutions for various typical requirements in practice. Having this in mind, we in this paper survey variants of the classical language based synthesis problems and develop respective solution algorithms. The presented methods may be seen as a large repertoire of synthesis procedures covering a lot of typical settings where synthesis is applicable.