Additional Study Information: This is a Phase 1 multicenter study of LY2606368, a CHK1/2 inhibitor, in pediatric patients with refractory solid tumors, including CNS tumors. The study treatment is considered experimental because LY2606368 is not approved by the United States (US) Food and Drug Administration (FDA) for treating pediatric patients with refractory solid tumors, including CNS tumors. The purpose of this study is to estimate the maximum tolerated dose of LY2606368. Another objective is to define its toxicities and potential antitumor activity. LY2606368, starting at Dose Level 1 = 80mg/m2, will be administered as an intravenous infusion over 60 minutes every 14 days of a 28-day cycle. Blood samples will be collected to determine how much LY2606368 is in the blood during the study (pharmacokinetics). Disease assessment will be completed before beginning treatment, at the end of Cycle 1, and then every other cycle.