GLIOMAS: As we demonstrated for supratentorial, diffuse gliomas in adults, a stratification into just two grades of malignancy, 'low' and 'high grade,' proved reliable and prognostically relevant. The discriminating histomorphological criterion for high-grade astrocytoma (WHO glioblastoma) as well as anaplastic oligodendroglioma and anaplastic oligoastrocytoma is endothelial hyperplasia/proliferation, which is usually associated with uptake of contrast medium in computed tomography and magnetic resonance imaging. As neoangiogenesis indicates glioma progression, it is worthwhile considering these radiographic features to judge the representativeness of the tumor samples critically. MENINGIOMAS: The revised edition of the WHO classification of brain tumors now includes the 'atypical' meningioma (WHO 'grade' II): Based on both its histomorphological features and prognosis, it should be placed between the common type and anaplastic meningioma. Nuclear area related Ki-67 proliferation indices, as determined by morphometry, were the prerequisite for outlining its histomorphological spectrum better. Cytogenetically, the most consistent progression-associated feature was loss of the distal part of the short arm of one chromosome 1 (1p-). Thus, a screening method using the tissue non-specific form of alkaline phosphatase (ALPL) as the respective marker enzyme was established. Diagnosing a meningioma of the intermediate type implies careful clinical and radiological patient follow-ups to detect tumor recurrences early.