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One of the most exciting developments in AdS/CFT in the past few years are the holographic complexity proposals. The latter conjucture that certain codimension-1 and codimension-0 bulk geometric objects are related to the hardness of preparing corresponding states on the boundary. A fascinating spin-off of this endavour are recent attempts to understand the properties of complexity in QFT with an eye of proving the holographic complexity proposals. The talk will provide an overview of some of these results and will focus on defining complexity for free QFTs and 2-dimensional CFTs, as well as properties of complexity in these setups. Based on 1707.08582, 1807.07075, 1810.05151 and 1904.02713.