Invasive alien insects cause serious ecological and economical losses around the world. Here, we review the bionomics, modern ranges (and their dynamics), distribution pathways, monitoring, and control measures of 14 insect species known to be important invasive and emerging tree pests in forest and urban ecosystems of Russia: Leptoglossus occidentalis (Hemiptera: Heteroptera: Coreidae), Halyomorpha halys (Hemiptera: Heteroptera: Pentatomidae), Corythucha arcuata (Hemiptera: Heteroptera: Tingidae), Agrilus fleischeri, A. mali, A. planipennis, Lamprodila (Palmar) festiva (Coleoptera: Buprestidae), Ips amitinus, Polygraphus proximus (Coleoptera: Curculionidae: Scolytinae), Cydalima perspectalis (Lepidoptera: Crambidae), Acrocercops brongniardella, Cameraria ohridella, Phyllonorycter issikii, and P. populifoliella (Lepidoptera: Gracillariidae). We identified three major scenarios of tree pest invasions in the country and beyond: (1) a naturally conditioned range expansion, which results in the arrival of a pest to a new territory and its further naturalization in a recipient region; (2) a human-mediated, long-distance transfer of a pest to a new territory and its further naturalization; and (3) a widening of the pest’s trophic niche and shift to new host plant(s) (commonly human-introduced) within the native pest’s range frequently followed by invasion to new regions.