Magnetic nanoparticle hyperthermia (MNH) is a localized cancer treatment that uses an alternating magnetic field to excite magnetic nanoparticles (MNPs) injected into a tumor, causing them to generate heat. Once the temperature of the tumor tissue reaches about 43 °C, the cancerous cells die. Different types of MNPs have been studied, including iron oxides with various coatings, Cu-Ni alloys, and complex manganese/zinc particles. This paper reviews different types of MNPs and assesses them by magnetization, specific absorption rate (SAR), and Curie temperature. We reviewed the achievements and limitations of the works in this field. A major issue with MNH is maintaining effective hyperthermia while preserving healthy tissue. Numerical modeling can predict temperature distribution and safely simulate hyperthermia. The most used bioheat transfer equation is Pennes' equation which includes a term for blood perfusion, an important factor for temperature distribution. While some models safely neglect it, most include the blood perfusion term. Some recent models have also included large blood vessels, others used their own heat transfer models. This article reviews the different models and classifies them based on how they address blood flow. A need for studies with realistic tumor shapes was identified. The irregular shape of most tumors could result in less uniform temperature distribution than in the commonly used circular or spherical models. This article aims to identify potential future work to create more realistic tumor models.