The main theme of this book is the study of the three-dimensional (3D) propagation dynamics of spatio-temporal wave packets. The Airy-Bessel wave packet is the main wave packet to be studied in the thesis. Other wave packets such as Airy-Airy-Airy and dual-Airy-Airy-rings are also investigated. An Airy-Bessel wave packet has been studied as a ``linear light bullet'' since it can propagate without dispersion or diffraction in the linear regime. An Airy-Airy-Airy wave packet also belongs to the family of ``linear light bullet''s. It has been studied both in the linear and the nonlinear regime. A dual-Airy-Airy-rings wave packet is a wave packet which has been just recently proposed. It can autofocus in an abruptly way which can be useful in some applications such as bio-imaging. For a dual-Airy-Airy-rings wave packet, to the best of our knowledge, it is the first time that such wave packet is experimentally generated. The 3D autofocusing effect is observed and measured in 3D.