Antiferromagnetic materials could represent the future of spintronic applications thanks to the numerous interesting features they combine: they are robust against perturbation due to magnetic fields, produce no stray fields, display ultrafast dynamics and are capable of generating large magneto-transport effects. Intense research efforts over the past decade have been invested in unraveling spin transport properties in antiferromagnetic materials. Whether spin transport can be used to drive the antiferromagnetic order and how subsequent variations can be detected are some of the thrilling challenges currently being addressed. Antiferromagnetic spintronics started out with studies on spin transfer, and has undergone a definite revival in the last few years with the publication of pioneering articles on the use of spin-orbit interactions in antiferromagnets. This paradigm shift offers possibilities for radically new concepts for spin manipulation in electronics. Central to these endeavors are the need for predictive models, relevant disruptive materials and new experimental designs. This paper reviews the most prominent spintronic effects described based on theoretical and experimental analysis of antiferromagnetic materials. It also details some of the remaining bottlenecks and suggests possible avenues for future research. Our review covers both spin-transfer-related effects, such as spin transfer torque, spin penetration length, domain wall motion and ‘magnetization’ dynamics; and spin-orbit related phenomena, such as (tunnel) anisotropic magnetoresistance, spin Hall and inverse spin galvanic effects. Effects related to spin-caloritronics, such as the spin Seebeck effect, are linked to the transport of magnons in antiferromagnets. The propagation of spin waves and spin superfluids in antiferromagnets are also covered.