Recent technological advances are based on effectively using complex multiphysics concepts. Therefore, there is an ever increasing need for accurate numerical al-gorithms of reduced complexity for solving multiphysics problems. Traditional mesh-based simulation methods depend on a neighbor connectivity information for formulation of operators like derivatives. In large deformation problems, de-pendence on a mesh could prove a limitation in terms of accuracy and cost of preprocessing. Meshless methods obviate the need to construct meshes thus al-lowing simulations involving severe geometric deformations such as breakup of a contiguous domain into multiple fragments. Smoothed Particle Hydrodynamics (SPH) is a meshless particle based Lagrangian numerical method that has the longest continuous history of development ever since it was introduced in 1977. Commensurate with the significant growth in computational power, SPH has been increasingly applied to solve problems of greater complexity in fluid mechanics, solid mechanics, interfacial flows and astrophysics to name a few. The SPH approximation of the continuity and momentum equations govern-ing fluid flow traditionally involves a stiff equation of state relating pressure and density, when applied to incompressible flow problems. Incompressible Smoothed Particle Hydrodynamics (ISPH) is a variant of SPH that replaces this weak com-pressibility approach with a pressure equation that gives a hydrostatic pressure field which ensures a divergence-free (or density invariant) velocity field. The present study explains the development of an ISPH algorithm and its implementa-tion with focus on application to free surface flows, interaction of fluid with rigid bodies and coupling of incompressible fluids with a compressible second phase. Several improvements to the exiting ISPH algorithm are proposed in this study. A semi-analytic free surface model which is more accurate and robust compared to existing algorithms used in ISPH methods is introduced, validated against experi-ments and grid based CFD results. A surface tension model with specific applica-bility to free surfaces is presented and tested using 2D and 3D simulations. Using theoretical arguments, a volume conservation error in existing particle methods in general is demonstrated. A deformation gradient based approach is used to derive a new pressure equation which reduces these errors. The method is ap-plied to both free surface and internal flow problems and is shown to have better volume conservation and therefore reduced density fluctuations. Also, comments on instabilities arising from particle distributions are made and the role of the smoothing functions in such instabilities is discussed. The challenges in imple-menting the ISPH algorithm in a computer code are discussed and the experience of developing an in-house ISPH code is described. A parametric study on water entry of cylinders of different shapes, angular velocity and density is performed and aspects such as surface profiles, impact pressures and penetration velocities are compared. An analysis on the energy transfer between the solid and the fluid is also performed. Low Froude number water entry of a sphere is studied and the impact pressure is compared with the theoretical estimates. The Incompressible SPH formulation, employing the proposed improvements from the study is then coupled with a compressible SPH formulation to perform two phase flow simulations interacting compressible and incompressible fluids. To gain confidence in its applicability, the simulations are compared against the theoretical predication given by the Rayleigh-Plesset equation for the problem of compressible drop in an incompressible fluid.