The present book addresses both advanced undergraduate or graduate students in mathematics who will participate in applied research. It might also be useful for the professional researchers in economics and biology, who use dynamical systems as modeling tools. In this book we try to provide procedures for applying general mathematical theory to concrete problems. Special attention is paid to numerical simulations. The applications from this book refer to the modeling of some processes from economy and biology. The models are described by differential equations with delay, stochastic differential equations with delay, uncertain differential equations with delay, fractional differential equations and fractional differential equation with delay in 1D, 2D and 3D.