Research of magnetoelectric effects and multiferroic materials, in which these effects are manifested, is among key areas in modern magnetism. This is associated with promising aspects of applying the results to spintronics, orbitronics, and new generation systems for information storage and processing. Despite a great many of already known materials which, in varying degrees, have magnetoelectric properties, the question regarding physical mechanisms and nature of magnetoelectric effects still remains open. Single-phase multiferroics with their magnetic and segnetoelectric properties implemented in a single crystalline phase are of especially great interest for studying. The most known "traditional multiferroics", such as bismuth ferrite, manganites, rare earthearth orthoferrites and orthochromites, fall into the class of perovskite multiferroics, i.e. the crystalline structure of ABO3 perovskites serve as their pre-phase. However, the difference between crystallographic distortions that results in the formation of various crystalline structures, for example, bismuth ferrite and rare-earth orthoferrites/orthochromites, leads to an essential difference in their physical properties, including magnetoelectric ones. Whereas bismuth ferrite characterized by the R3c symmetry space group is a segnetoelectric (i.e. it has spontaneous segnetoelectric polarization), the presence of segnetoelectric polarization in orthoferrites/orthochromites with the Pbnm symmetry space group is impossible from the symmetry standpoint. However, recent experimental and theoretical research works show that under certain conditions magnetoelectric properties are found in both classes of the said multiferroics. This paper is an overview by its nature and discusses magnetoelectric effects in various classes of single-phase multiferroics with the distorted perovskite structure: proper multiferroics exemplified by bismuth ferrite and improper multiferroics exemplified by rare-earth orthoferrites/orthochromites. Consideration is given to basic principles of the symmetry approach used to study magnetoelectric effects in multiferroics; calculations and analysis of magnetoelectric effects in rare-earth orthoferrites/orthochromites are performed through the methods of group-theoretical analysis.