Bio-mechanical hybrids are an emerging class of engineered composite soft materials with the ability to move and reconfigure their structure and properties in response to external stimuli. Similar to their biological counterparts, they can transduce energy stored in the environment to drive systematic movements. This functionality is critical for a variety of applications, from bioinspired micromachines and sensors to self-assembled microrobots. Here, by combining two seemingly incompatible concepts, living swimming bacteria and inanimate but orientationally ordered lyotropic liquid crystal, we conceive a fundamentally new class of matter - living liquid crystals (LLCs). LLCs can be actuated and controlled by the amount of oxygen available to bacteria, by concentration of ingredients or by the temperature. Our studies reveal a wealth of intriguing phenomena, caused primarily by the coupling between the activity-triggered flows and director reorientations. Among these are (a) coupling between the orientation and degree of order of LLC and the bacterial motion, (b) local nematic-isotropic phase transition caused by the bacteria-produced shear flows, (c) periodic stripe instabilities of the director in surface-anchored LLCs, (d) director pattern evolution into an array of disclinations with positive and negative topological charges as the surface anchoring is weakened or when the bacterial activity is enhanced; (e) direct optical visualization and quantitative characterization of microflows generated by the nanometers-thick bacterial flagella by the birefringent LLC medium. Our work suggests an unorthodox design concept of reconfigurable microfluidic chambers for control and manipulation of bacteria. Besides an obvious importance to active matter, our studies can result in valuable biosensing and biomedical applications.