We will review our recent work on the growth dynamics of molecular semiconductors by organic molecular beam deposition (OMBD), with emphasis on growth studies beyond the first monolayer, i.e. the evolution of the film structure and morphology. After briefly discussing general issues related to growth modes, correlation functions, dynamic scaling, and growth exponents, we will try to identify the general features that distinguish organic from inorganic systems, such as the different interaction potentials and the internal degrees of freedom of organic molecules.@footnote 1@ We will then discuss selected case studies of perylene-derivatives (in particular diindeno-perylene (DIP)@footnote 2@ and 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA)@footnote 3@), with results on the dynamic scaling exponents and real-time studies of the growth. Finally, we will briefly discuss the implications for organics-based heterostructures and the improvement of device performance. @FootnoteText@@footnote 1@F. Schreiber, Phys. Stat. Sol. (a) 201 (6) (2004) 1037 @footnote 2@A. C. Dürr et al., Phys. Rev. Lett. 90 (2003) 016104 @footnote 3@B. Krause et al., Europhys. Lett. 65 (3) (2004) 372