Conventional designs of an avalanche photodiode (APD) have been based on a planar p–n junction since the 1960s. APD developments have been driven by the necessity to provide a uniform electric field over the active junction area and to prevent edge breakdown by special measures. Most modern silicon photomultipliers (SiPM) are designed as an array of Geiger-mode APD cells based on planar p–n junctions. However, the planar design faces an inherent trade-off between photon detection efficiency and dynamic range due to loss of an active area at the cell edges. Non-planar designs of APDs and SiPMs have also been known since the development of spherical APDs (1968), metal-resistor-semiconductor APDs (1989), and micro-well APDs (2005). The recent development of tip avalanche photodiodes (2020) based on the spherical p–n junction eliminates the trade-off, outperforms the planar SiPMs in the photon detection efficiency, and opens new opportunities for SiPM improvements. Furthermore, the latest developments in APDs based on electric field-line crowding and charge-focusing topology with quasi-spherical p–n junctions (2019–2023) show promising functionality in linear and Geiger operating modes. This paper presents an overview of designs and performances of non-planar APDs and SiPMs.