This is a traditional phase I dose finding study to estimate the maximum tolerated dose (MTD) and describe the dose limiting toxicities (DLT) of the combination of bevacizumab, administered every 2 weeks IV and everolimus administered orally daily to children with recurrent or refractory solid tumors including CNS malignancies. Patients will receive bevacizumab every two weeks IV, and everolimus orally daily. Four consecutive weeks will constitute one course and subsequent courses will immediately follow with no break in the administration of either drug. In the absence of disease progression or unacceptable toxicity, treatment can continue for 2 years. The bevacizumab dose will start at 10 mg/kg. Everolimus will start at 4 mg/m2, 80% of the MTD established in our current phase I trial. A traditional 3+3 dose escalation/de-escalation design will be used to determine the joint MTD for these two agents. Doses to be studied are detailed in the table below. Consistent with the traditional design, we will enroll cohorts of 3 patients at each dose level starting with dose level 1 and will escalate to the next higher dose, if none of these 3 experiences a DLT. If one of 3 patients experiences a DLT at a dose level then 3 more patients will be studied at this level. If none of these 3 experiences a DLT then escalation to the next level will occur. Otherwise the current dose will be considered too toxic and de-escalation will occur. Under this setting, MTD will be the dose level at which 0/3 or 1/6 patient would have experienced DLT and the next dose level is determined to be too toxic.