Three-dimensional (3D) printing of hydrogels is now an attractive area of research due to its capability to fabricate intricate, complex and highly customizable scaffold structures that can support cell adhesion and promote cell infiltration for tissue engineering. However, pure hydrogels alone lack the necessary mechanical stability and are too easily degraded to be used as printing ink. To overcome this problem, significant progress has been made in the 3D printing of hydrogel composites with improved mechanical performance and biofunctionality. Herein, we provide a brief overview of existing hydrogel composite 3D printing techniques including laser based-3D printing, nozzle based-3D printing, and inkjet printer based-3D printing systems. Based on the type of additives, we will discuss four main hydrogel composite systems in this review: polymer- or hydrogel-hydrogel composites, particle-reinforced hydrogel composites, fiber-reinforced hydrogel composites, and anisotropic filler-reinforced hydrogel composites. Additionally, several emerging potential applications of hydrogel composites in the field of tissue engineering and their accompanying challenges are discussed in parallel.