Several specimens of Lauraceae fossil wood from the Cenozoic of Greece (southern part of Lesbos), the Czech Republic (Kadaň-Zadní Vrch Hill and Jáchymov), and Hungary (Ipolytarnóc) were studied. When considering whether they belonged to the speciose fossil wood genus Laurinoxylon, we reviewed the literature and data from InsideWood on fossil and modern woods. As a result, we propose criteria for excluding a fossil Lauraceae wood from Laurinoxylon and list the species that should be excluded from this genus. The criteria (filters) proposed to exclude a genus from having relationships with Laurinoxylon are: A. Axial parenchyma features: A1. Marginal axial parenchyma, A2. Aliform to aliform-confluent paratracheal parenchyma. B. Ray features: B1. Rays higher than 1 mm, B2. Exclusively homocellular rays, B3. Rays more than 5 cells wide, B4. Rays storied. C. Porosity features: Ring-porous. D. Idioblasts: Absence of idioblasts. Based on the distribution of idioblasts, we recognize four groups in Laurinoxylon (Type 1 - with idioblasts associated only with ray parenchyma cells, Type 2a - with idioblasts associated with both ray and axial parenchyma, Type 2b - with idioblasts associated both with rays and present among the fibres, and Type 3 - with idioblasts associated with ray and axial parenchyma and also among the fibres) and list the extant genera with features of those groups. Such grouping helps with interpreting the relationships of fossil lauraceous woods with extant genera. We discuss the Oligocene–Miocene European species that belong to these Laurinoxylon groups, noting that some warrant reassignment to different genera or even families. Future studies are needed to determine whether new genera should be established to accommodate these species. We propose the new combination Cinnamomoxylon variabile (Privé-Gill & Pelletier) Mantzouka, Karakitsios, Sakala & Wheeler.