Thermodynamics is the science of heat engines, or more fundamentally, science of energy, focusing on the interplay between heat and work. It is developed to deal with macroscopic systems, yet there is recent interest to built engines in microscopic limits. It is therefore necessary to examine thermodynamics in quantum regime. Exploration of quantum analogs of classical heat engines can be traced back to the recognition of maser as an Otto engine in 50s. Since then, quantum dots, trapped ions, spin systems, atomic condensates, optical cavities, quantum Hall systems, optomechanical resonators, and relativistic particles are considered as working substances for quantum heat engines (QHEs). Profound quantum effects emerge when quantum heat reservoirs are included. If quantum heat bath has quantum coherence, entanglement, or squeezing, QHE can surpass the Carnot bound. Observation of quantum advantages is challenged due to decoherence. However, quantum coherence is argued to survive in ambient temperatures in some biological processes, such as photosynthesis, being responsible for the ballistic transfer of energy. Information feedback from the environment could help to maintain coherence in these processes. Such an environment has a memory and called a non-Markovian reservoir. It is suggested for longevity of quantum memories, a crucial ingredient for quantum communication and quantum computation. Despite the analogies between QHEs and quantum information devices, there are only a few studies of non-Markovian reservoirs for QHEs. Our fundamental purpose is to establish mechanical equivalent of non-Markovian resources. Our practical purpose is to propose an optimum QHE that can use non-Markovian resources with capabilities surpassing classical counterparts.