The electron spin made its debut in the device world only two decades ago but today our ability of detecting the spin state of a moving electron underpins the entire magnetic data storage industry. This technological revolution has been driven by a constant improvement in our understanding on how spins can be injected, manipulated and detected in the solid state, a field which is collectively named Spintronics. Recently a number of pioneering experiments and theoretical works suggest that organic materials can offer similar and perhaps superior performances in making spin-devices than the more conventional inorganic metals and semiconductors. Furthermore they can pave the way for radically new device concepts. This is Molecular Spintronics, a blossoming research area aimed at exploring how the unique properties of the organic world can marry the requirements of spin-devices. Importantly, after a first phase, where most of the research was focussed on exporting the concepts of inorganic spintronics to organic materials, the field has moved to a more mature age, where the exploitation of the unique properties of molecules has begun to emerge. Molecular spintronics now collects a diverse and interdisciplinary community ranging from device physicists to synthetic chemists to surface scientists. In this critical review, I will survey this fascinating, rapidly evolving, field with a particular eye on new directions and opportunities. The main differences and challenges with respect to standard spintronics will be discussed and so will be the potential cross-fertilization with other fields (177 references).