The strain engineering effects induced by different means, e.g., the substrate lattice mismatch and/or chemical doping, on the functional properties of perovskite thin films have triggered interest in the use of these materials in different applications such as energy storage/generation or photonics. The effects of the film’s thickness and strain state of the structure for the lead-free perovskite ferrite-based materials (BiFeO3-BFO; Y-doped BiFeO3-BYFO; LaFeO3-LFO) on their functional properties are highlighted here. As was previously demonstrated, the dielectric properties of BFO epitaxial thin films are strongly affected by the film thickness and by the epitaxial strain induced by the lattice mismatch between substrate and film. Doping the BiFeO3 ferroelectric perovskite with rare-earth elements or inducing a high level of structural deformation into the crystalline structure of LaFeO3 thin films have allowed the tuning of functional properties of these materials, such as dielectric, optical or photocatalytic ones. These changes are presented in relation to the appearance of complex ensembles of nanoscale phase/nanodomains within the epitaxial films due to strain engineering. However, it is a challenge to maintain the same level of epitaxial strain present in ultrathin films (<10 nm) and to preserve or tune the positive effects in films of thicknesses usually higher than 30 nm.