The purpose of this study is to test any good and bad effects of the study drugs called ruxolitinib and thalidomide. Ruxolitinib and thalidomide could shrink the cancer, but it could also cause side effects.

Inclusion Criteria:

• Diagnosis of myelofibrosis (either primary or post essential thrombocythemia/polycythemia vera) requiring therapy, including those previously treated and relapsed or refractory, or if newly diagnosed, with intermediate-1 or -2 or high risk IPSS, DIPSS, DIPSS+, MIPSS70 or MIPSS70+ v2.0 score

• Patients taking Ruxolitinib at the time of enrollment must have been taking Ruxolitinib for a minimum of 3 months, and must have been on a stable dose of Ruxolitinib for a minimum of 4 weeks immediately prior to enrollment. However, for patients in the thrombocytopenic cohort A expansion, patients taking Ruxolitinib at the time of enrollment who are deemed to have a suboptimal response or are refractory to Ruxolitinib single-agent therapy (less than partial response per IWG criteria) must have been taking Ruxolitinib for a minimum of 6 weeks, and must have been on a stable dose of Ruxolitinib for a minimum of 4 weeks immediately prior to enrollment

• Patients taking Ruxolitinib at the time of enrollment must be deemed to have had a suboptimal response (less than partial response per IWG criteria) to Ruxolitinib single-agent therapy or deemed to have progression of disease (per IWG criteria).

• Age ≥ 18 years at the time of signing the informed consent.

• ECOG performance status 0 to 2.

• Patients must have adequate organ function as demonstrated by the following:

  1. Total bilirubin ≤ 2.0 mg/dL, unless due to Gilbert's disease
  2. Serum creatinine ≤ 2.0 mg/dL.
  3. ALT and AST ≤ 3 x upper limit of normal (unless the transaminitis is considered to be related to MF, in which case ≤5 x ULN is allowed

• Females of childbearing potential (FCBP)† must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL within 14 days prior to and again within 24 hours* of starting Thalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 4 weeks before she starts taking Thalidomide. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a condom during sexual contact with a female of child bearing potential even if they have had a successful vasectomy. All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure.

• All study participants must be registered into the mandatory REMS® program, and be willing and able to comply with the requirements of REMS®

• Platelets ≥ 50000/uL and ANC ≥ 1000. For patients enrolled in the thrombocytopenic cohorts, platelet count must be >/= 25,000 but \