Recent progress in microspherical superlens nanoscopy raises a fundamental question about the transition from super-resolution properties of mesoscale microspheres, which can provide a subwavelength resolution Formula: see text, to macroscale ball lenses, for which the imaging quality degrades because of aberrations. To address this question, this work develops a theory describing the imaging by contact ball lenses with diameters Formula: see text covering this transition range and for a broad range of refractive indices Formula: see text. Starting from geometrical optics we subsequently proceed to an exact numerical solution of the Maxwell equations explaining virtual and real image formation as well as magnification M and resolution near the critical index Formula: see text which is of interest for applications demanding the highest M such as cellphone microscopy. The wave effects manifest themselves in a strong dependence of the image plane position and magnification on Formula: see text, for which a simple analytical formula is derived. It is demonstrated that a subwavelength resolution is achievable at Formula: see text. The theory explains the results of experimental contact-ball imaging. The understanding of the physical mechanisms of image formation revealed in this study creates a basis for developing applications of contact ball lenses in cellphone-based microscopy.