This paper reviews recent applications of well-defined silica-supported hydrides of the group 4 and 5 transition metals in the held of carbon-carbon and carbon-hydrogen bonds activation of alkanes. The synthesis and characterization of the zirconium and tantalum hydrides is presented. (=SiO)(3)M-H complexes (M=Ti 1, Zr 2, Hf 3) are obtained by hydrogen treatment at c.a. 150 degrees C of =Si-O-MNp3 (Np=CH2C(CH3)(3)). These three surface complexes are formally 8 electrons species and are consequently very electrophilic. (=SiO)(2)Ta-H 4 is obtained by hydrogen treatment at c.a. 150 degrees C of (=Si-O)(x)Ta(=CHC(CH3)(3))(CH2C(CH3)(3))(3-x) (x=1,2) and is also highly electrophilic. Examples of applications of these hydrides in the field of the activation of alkanes at moderate temperatures are then given. The complexes 1-3 can achieve the hydrogenolysis of alkanes at low temperature. With 1 a simultaneous reaction of skeletal isomerization occurs. With 2 and 3 the mechanism of C-C bond cleavage passes through an elementary step of beta-alkyl transfer. The mechanism of hydroisomerization observed with 1 passes also by an elementary step of beta-alkyl transfer but in this case the beta-H elimination-olefin reinsertion occurs quite rapidly so that a skeletal isomerization also occurs. Complexes of type 2 or 3 were found to catalyze under olefin pressure the olefin polymerization, and under hydrogen pressure, the polyolefin hydrogenolysis. Here the equilibrium between the olefin insertion into a metal-alkyl and the beta-alkyl transfer is shown to occur with the same catalyst in agreement with the concept of microreversibility. A new catalytic reaction, called "alkane metathesis" has been discovered with complex 4. By this reaction alkanes are catalytically transformed into higher and lower alkanes. The mechanism by which this reaction occurs is not fully understood. The products distribution, especially with labeled alkanes is explained by a concerted mechanism by which a Ta-C bond and a C-C bond of the alkane can be cleaved and reformed simultaneously via a kind of four centered sigma-bond metathesis which has no precedent in classical organometallic chemistry.