Systematic studies on polycrystalline Hf1–xZrxO2 films with varying Zr contents show that HfO2 films are paraelectric (monoclinic). If the Zr content is increased, films become ferroelectric (orthorhombic) and then antiferroelectric (tetragonal). HfO2 shows very good insulating properties and it is used in metal-oxide-semiconductor field-effect devices, while ZrO2 shows good piezoelectric properties, but it is antiferroelectric. In between, Hf0.5Zr0.5O2 shows good ferroelectric properties at the expense of poorer insulating and piezoelectric properties than HfO2 and ZrO2, respectively. Here, we explore the ferroelectric, insulating, and piezoelectric properties of a series of epitaxial films of Hf1–xZrxO2 with different compositions. We show that epitaxial growth permits the stabilization of the ferroelectric phase in a whole range of Zr content (from x = 0 to x = 1). In epitaxial ZrO2 films, ferroelectricity coexists with better piezoelectric and insulating properties than Hf0.5Zr0.5O2, and in HfO2 epitaxial films, ferroelectricity coexists with better insulating properties than Hf0.5Zr0.5O2. For the case of ZrO2 films, large electroresistance is also observed. In both cases, the ferroelectric endurance is poorer than that for Hf0.5Zr0.5O2. Financial support from the Spanish Ministerio de Ciencia e Innovación, through the “Severo Ochoa” FUNFUTURE (CEX2019-000917-S) and the MAT2017-85232-R (AEI/ FEDER, EU), PID2019-107727RB-I00 (AEI/FEDER, EU), PID2020-112548RB-I00, and MAT2015-73839-JIN projects, from Generalitat de Catalunya (2017 SGR 1377), and from the French National Research Agency (ANR) through the projects MITO (ANR-17-CE05-0018-01), LILIT (NR-16-CE24- 0022), and DIAMWAFEL (ANR-15-CE08-0034-02) is acknowledged. I.F. acknowledges Ramón y Cajal contract RYC-2017-22531. The project was supported by a 2020 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. T.S. and H.T. are financially supported by China Scholarship Council (CSC) with nos. 201807000104 and 201906050014, respectively. Work of T.S. and H.T. has been done as a part of their Ph.D. program in Materials Science at Universitat Autonoma de Barcelona. Peer reviewed