The spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) resulted in an extraordinary global public health crisis. In early 2020, Cyprus, among other European countries, was affected by the SARS-CoV-2 epidemic and adopted lockdown measures in March 2020 to limit the initial outbreak on the island. In this study, we performed a comprehensive retrospective molecular epidemiological analysis (genetic, phylogenetic, phylodynamic and phylogeographic analyses) of SARS-CoV-2 isolates in Cyprus from April 2020 to January 2021, covering the first ten months of the SARS-CoV-2 infection epidemic on the island. The primary aim of this study was to assess the transmissibility of SARS-CoV-2 lineages in Cyprus. Whole SARS-CoV-2 genomic sequences were generated from 596 clinical samples (nasopharyngeal swabs) obtained from community-based diagnostic testing centers and hospitalized patients. The phylogenetic analyses revealed a total of 34 different lineages in Cyprus, with B.1.258, B.1.1.29, B.1.177, B.1.2, B.1 and B.1.1.7 (designated a Variant of Concern 202012/01, VOC) being the most prevalent lineages on the island during the study period. Phylodynamic analysis showed a highly dynamic epidemic of SARS-CoV-2 infection, with three consecutive surges characterized by specific lineages (B.1.1.29 from April to June 2020; B.1.258 from September 2020 to January 2021; and B.1.1.7 from December 2020 to January 2021). Genetic analysis of whole SARS-CoV-2 genomic sequences of the aforementioned lineages revealed the presence of mutations within the S protein (L18F, DeltaH69/V70, S898F, DeltaY144, S162G, A222V, N439K, N501Y, A570D, D614G, P681H, S982A and D1118H) that confer higher transmissibility and/or antibody escape (immune evasion) upon the virus. Phylogeographic analysis indicated that the majority of imports and exports were to and from the United Kingdom (UK), although many other regions/countries were identified (southeastern Asia, southern Europe, eastern Europe, Germany, Italy, Brazil, Chile, the USA, Denmark, the Czech Republic, Slovenia, Finland, Switzerland and Pakistan). Taken together, these findings demonstrate that the SARS-CoV-2 infection epidemic in Cyprus is being maintained by a continuous influx of lineages from many countries, resulting in the establishment of an ever-evolving and polyphyletic virus on the island.