This review paper describes the destructive and non-destructive measurements implemented or under development at CEA, in view to perform the most complete radioactive waste characterization. First, high-energy photon imaging (radiography, tomography) brings essential information on the waste packages, such as density, position and shape of the waste inside the container and in the possible binder, quality of coating and blocking matrices, presence of internal shields or structures, presence of cracks, voids, or other defects in the container or in the matrix, liquids or other forbidden materials, etc. Radiological assessment is then performed using a series of non-destructive techniques such as gamma-ray spectroscopy, which allows characterizing a wide range of radioactive and nuclear materials, passive neutron coincidence counting and active neutron interrogation with the differential die-away technique, or active photon interrogation with high-energy photons (photofission), to measure nuclear materials. Prompt gamma neutron activation analysis (PGNAA) can also be employed to detect toxic chemicals or elements which can greatly influence the above measurements, such as neutron moderators or absorbers. Digital auto-radiography can also be used to detect alpha and beta contaminated waste. These non-destructive assessments can be completed by gas measurements, to quantify the radioactive and radiolysis gas releases, and by destructive examinations such as coring homogeneous waste packages or cutting the heterogeneous ones, in view to perform visual examination and a series of physical, chemical, and radiochemical analyses on samples. These last allow for instance to check the mechanical and containment properties of the package envelop, or of the waste binder, to measure toxic chemicals, to assess the activity of long-lived radionuclides or pure beta emitters, to determine the isotopic composition of nuclear materials, etc.