For example, bismuth ferrite (BiFeO 3 or BFO) perovskite, which is likely the most studied multiferroic system to date because of its large polarization and high ordering temperatures, [9,10] has a relatively weak magnetoelectric coupling in its bulk form [11] (which adopts the so-called R-phase [12] ), which hinders its technical application. Similarly, the other intensively studied class of multiferroics formed by hexagonal ReMnO 3 and ReFeO 3 materials, where Re is a rare-earth or the Y ion (see, e.g., refs. [13] and [14] and references therein), has a relatively small value for their out-of-plane polarization (e.g., ≈6 µC cm −2 in YMnO 3 [15,16] ) due to their improper character, which may be a disadvantage to their utilization in devices.As a result, searching for novel multiferroic materials or even novel phases in already known multiferroics constitutes an active research activity. [12,[17][18][19][20][21][22][23] For instance, the discovery of a novel multi ferroic phase, the so-called T-phase, in BFO systems grown as thin films along the pseudocubic [001] direction and under large compressive strain [12,24] has generated a large interest, especially since large magnetoelectric effects have been predicted to occur near the strain-induced boundary between the R and T phases. [25,26] Based on the aforementioned findings and the fact that paraelectric magnetic perovskites made of ReFeO 3 have been recently predicted to transform into polar hexagonal YMnO 3 -type phases (and thus to become multiferroic) when grown on top of (111) cubic or (0001) hexagonal substrates exercising a large enough tensile strain, [27] it is legitimate to wonder if such latter, rather atypical for now, conditions of growth and epitaxial strain can also give rise to novel multiferroic phases and effects in BFO films.The goal of this paper is to reveal that epitaxial (111) BiFeO 3 films are indeed predicted to adopt new multiferroic phases when placed under large enough tensile strain. For instance, they can exhibit not only the polar hexagonal YMnO 3 -type configuration but also another brand new crystal structure of triclinic symmetry. These hexagonal and triclinic states are further numerically found to display unusual properties, such as an out-of-plane polarization anomalously increasing when increasing tensile epitaxial strain (due to the appearance of a proper ferroelectric character) and an electrically controllable spiral magnetism, respectively. In particular, the presently determined triclinic structure appears to be rather promising to induce strong or novel magnetoelectric effects, due to the fact Multiferroics are attracting much interest because they simultaneously possess ordered electric and magnetic dipoles. In particular, numerous recent studies are devoted to find novel multiferroic phases, as, for example evidenced by the flurry of activities that accompanied the discovery of the so-called T-phase in BiFeO 3 systems, when these latter are made in forms of (001) epitaxial films and subject to high-enough compressi...