Materials that have at least two coupled electric, magnetic, and structural order parameters resulting in simultaneous ferroelectricity, ferromagnetism, and ferroelasticity are known as multiferroic materials. Bismuth ferrite (BiFeO3) is one of the most heavily studied room temperature single-phase multiferroic material. The simultaneous existence of ferroelectricity and antiferromagnetism with cross-coupling between these order parameters has driven intense research to accomplish electric field control of magnetism. To utilize these materials in electronic applications it is desirable to increase the magnetization and magnetoelectric coupling while reducing the switching voltage and leakage current. Tuning these responses can be achieved via strain and/or elemental engineering techniques. As the former is limited by the availability of suitable high-quality substrates for control of strain state, the latter is a more flexible technique. This thesis focuses on a systematic study of growth, structural, electrical, and magnetic characterizations of epitaxial thin films of multiferroic BiFeO3 (BFO) and Fe-site substituted BiFeO3. High-quality multiferroic epitaxial films of BiFeO3 on SrRuO3 buffered(001)-oriented SrTiO3 substrates fabricated using pulsed laser deposition are investigated. Switching dynamics of BiFeO3 have been explored using three fundamental scaling laws: Kittel's law, Kay-Dunn law, and the Ishibashi-Orihara model to acquire a complete description of the dynamical behavior and its relationship to the microstructure of the films. The primary goal of this work is to explore Fe-site substitution with magnetic elements Co and Mn, and non-magnetic element Al in BFO over a wide range of compositions. The enhancement of piezoelectric properties, electrical conductivity, and magnetic properties have been achieved through cobalt substitution. On the other hand, reduction in leakage current, and enhancement in magnetic and piezoelectric properties have been achieved through Al substitution. Moreover, we analyzed the switching dynamics in the time domain and corroborated the findings with the domain structure via a microscopy technique. It is demonstrated that Fe-site substitution of BFO is indeed a viable option to achieve improved characteristics required for device use. By identifying thebenefits of Fe-site substitution, this dissertation provides a pathway to explore BFO-based alternate magnetoelectric materials with desired properties for device applications.