Most of the real world problems can be modeled with differential equations. Systems of ODEs have applications in many fields of research, including economics, engineering, biology, chemistry, and physics. In the rapidly expanding field of mathematical biology, we can refer to recent research in biochemistry [2], neuroscience [12], epidemiology [6], and immunology [15], among others. They may be studied by using bifurcation theory and numerical methods. Numerical analysis of bifurcations requires special computations (e.g. continuation and normal form computations, construction of auxiliary maps and computing dimensional characteristics of attractors), which should be performed interactively. Therefore, bifurcation analysis should combine theoretical results, efficient numerical methods, and a user-friendly graphical interface. Bifurcation softwares are essential tools in the study of dynamical systems. From the beginning (the first packages were written in the 1970’s), bifurcation softwares have also been used in the modelling processes. In its simplest form, this involves tuning the parameters of the system in such a way that the right bifurcations with the right properties (for example, a supercritical Hopf bifurcation) are found at the correct place, as a strong indication that the mathematical model behaves correctly. Examples of this strategy are given in dir=ltr This thesis is organized as follows. In Chapter 1, in Section 1 we review the existing general-purpose tools for bifurcation analysis, and provide a survey of the provided functionalities. Also, in Section 2 we give an overview of MATCONT and its features. In Chapter 2, we introduce continuous-time dynamical systems and corresponding bifurcation theory. In Chapter 3, we describe some of the basic techniques used in the numerical analysis of dynamical systems. Particularly we focus on algorithms that are more specific to bifurcation analysis, specifically those for the location of equilibria (fixed points) and their continuation with respect to parameters, and for the detection, analysis, and continuation of codimention-1 bifurcations. Special attention is given to location and continuation of limit cycles and their associated bifurcations. Chapter 4 is devoted to study bifurcations of equilibria and their continuation under variation of two parameters and computations of codimention-2 bifuracation points along these curves. Chapter 5, having a similar structure, we introduce codimention-1 bifuracatio of limit cycles and their continuation under variation of one parameter by using minimally extended systems. Finally Chapter 6 discusses software issues that are particularly important for many users, e.g. how to define a new system starting from an existing one, how to import and export data, system descriptions, and computed results. Furthermore by using MATCONT toolbox some examples are studied and their bifurcations are computed and continued numerically. MATCONT and CL_MATCONT are freely available MATLAB numerical continuation packages for the interactive study of dynamical systems and bifurcations. MATCONT is the GUI-version, CL_MATCONT is the command-line version. MATCONT and CL_MATCONT are freely available at https://www.matcont.UGent.be.