Inclusion Criteria:
Parts 1 and 2:
* Navitoclax Monotherapy (Part 1 Only - Japanese Participants):
* Documented diagnosis of myelofibrosis (MF), polycythemia vera (PV) or essential thrombocythemia (ET) as defined by the World Health Organization (WHO) classification.
* MF participants must have received and failed or are intolerant to ruxolitinib therapy.
* ET or PV participants must be requiring cytoreduction who have failed or are intolerant to at least one prior therapy, or who refuse standard therapy.
* Navitoclax + ruxolitinib Combination Therapy (Part 2 Only - Japanese and Taiwanese Participants):
* Has documented diagnosis of primary MF, post-polycythemia vera MF (PPV-MF), or post-essential thrombocythemia (PET-MF) as defined by the World Health Organization (WHO) classification.
* Is ineligible or unwilling to undergo stem cell transplantation at time of study entry.
* Has splenomegaly as defined by a spleen palpable \>= 5 cm below costal margin or spleen volume \>= 450 cm\^3 as assessed by magnetic resonance imaging (MRI) or computed topography (CT) scan.
* Must have received ruxolitinib therapy for at least 12 weeks and be currently on a stable dose of ruxolitinib (as described in the protocol).
* Must have adequate bone marrow, kidney, liver and hematology blood values as detailed in the study protocol.
* Part 1 only: Cytoreduction for participants with ET and PV therapy within 14 days prior to the first dose of navitoclax will be allowed pending additional discussion with study doctor. Ruxolitinib for MF participants will not be allowed within 7 days prior to the first dose of study drug and during navitoclax administration.
* Eastern Cooperative Oncology Group (ECOG) performance status \<= 1.
Part 3, and Part 4 (Participants in US and Europe):
* Part 3 Only: At screening or baseline (pre-dose on Day 1), participant has QT interval corrected for heart rate (QTc) interval by Fridericia's correction (QTcF) \<= 450 msec.
* Participants with a documented diagnosis of primary or secondary MF, ET, PV or chronic myelomonocytic leukemia (CMML) as defined by the WHO classification.
* Participants must be requiring treatment and have failed or are intolerant to at least one prior therapy or who refuse standard therapy.
* ECOG performance status \<= 2.
* Must have adequate bone marrow, kidney, liver and hematology blood values as detailed in the study protocol.
Part 5 (Participants in US and Europe):
* Has a documented diagnosis of primary MF as defined by the WHO classification, post-polycythemia vera (PV) MF, or post-essential thrombocythemia (ET) MF.
* Classified as intermediate-2 or high-risk MF, as defined by the Dynamic International Prognostic Scoring System (DIPSS).
* Requiring treatment for MF and must either have no prior treatment with a JAK2 inhibitor or have received treatment with ruxolitinib as noted in the protocol.
* Have an ECOG performance status \<=2.
* Have adequate bone marrow, kidney, liver and hematology blood values as detailed in the protocol.
Exclusion Criteria:
Part 1 and 2:
* Shows leukemic transformation (\> 10% blasts in peripheral blood or bone marrow biopsy).
* Has a history of an active malignancy other than MPN within the past 2 years prior to study entry (exceptions detailed in the protocol).
* Has a positive test result for HIV at screening.
* Has chronic active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection requiring treatment.
* Has evidence of other clinically significant uncontrolled condition(s).
* Has previously taken a BH3 mimetic compound.
* Currently on medications that interfere with coagulation (including warfarin) or platelet function with the exception of low dose aspirin (up to 100 mg) and low-molecular-weight heparin (LMWH).
* Has received strong or moderate CYP3A inhibitors (e.g., ketoconazole, clarithromycin) within 14 days prior to the administration of the first dose of navitoclax.
Part 3, and Part 4:
* Had prior therapy with a BH3 mimetic compound.
* Have received strong or moderate CYP3A inhibitors within 28 days or 5 half-lives of the drug (whichever is shorter) prior to the first dose of navitoclax.
* Have received strong CYP3A inducers within 10 days prior to the first dose of navitoclax.
* Show leukemic transformation (\> 10% blasts in peripheral blood or bone marrow biopsy).
* Currently on medications that interfere with coagulation (including warfarin) or platelet function except for low-dose aspirin (up to 100 mg) and LMWH.
Part 4 Only:
* Have received CYP2C9 inhibitors within 28 days or 5 half-lives of the drug (whichever is shorter) prior to the first dose of study drugs.
* Have received CYP2C9 inducers within 10 days prior to the first dose of study drugs.
Part 5 Only:
* Have accelerated MF, defined as \> 10% blasts in peripheral blood or bone marrow aspirate and biopsy.
* Eligible for stem cell transplantation at time of study entry.
* Had prior therapy with a BH3 mimetic compound or BET inhibitor.
* Currently on medications that interfere with coagulation (including warfarin) or platelet function except for low-dose aspirin (up to 100 mg) and LMWH.
* Have received strong CYP3A inhibitors or CYP2C9 inhibitors within 28 days of 5 half-lives of the drug (whichever is shorter) prior to the first dose of study drugs.
* Have received strong CYP3A inducers or CYP2C9 inducers within 10 days prior to the first dose of study drugs.
