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The complex geometry deals with complex manifold which is a core of contemporary research in differential geometry. Over the last few decades, work in the field of complex manifold was slow. A. Gray worked on the basic structures of complex manifolds, such as Hermitian manifolds, nearly Kaehler manifolds, etc. S. Ishihara studied quaternion Kaehlerian manifolds. A. Bejancu generalized this notion in a very good manner and studied Geometry of CR-submanifolds. But B.Y. Chen in 1990, generalized the concept and established Geometry of slant submanifolds. Afterwards, several geometers tried to work on the generalized structure of complex manifolds. In this book, it has been tried to generalize the concept on complex manifolds. The initial chapters establish inequalities between the Ricci curvature and the squared mean curvature, B.Y. Chen inequalities for certain slant submanifolds and also establishes an inequality between the warping function and the squared mean curvature for totally real warped product submanifolds. This book tells about the study of certain structures of slant, semi-slant and bi-slant submanifolds in generalized complex space forms and in quaternion space forms.