This paper examines telomeres from an evolutionary perspective. In the monocot plant order Asparagales two evolutionary switch-points in telomere sequence are known. The first occurred when the Arabidopsis-type telomere was replaced by a telomere based on a repeat motif more typical of vertebrates. The replacement is associated with telomerase activity, but the telomerase has low fidelity and this may have implications for the binding of telomeric proteins. At the second evolutionary switch-point, the telomere and its mode of synthesis are replaced by an unknown mechanism. Elsewhere in plants (Sessia, Vestia, Cestrum) and in arthropods, the telomere "typical" of the group is lost. Probably many other groups with "unusual" telomeres will be found. We question whether telomerase is indeed the original end-maintenance system and point to other candidate processes involving t-loops, t-circles, rolling circle replication and recombination. Possible evolutionary outcomes arising from the loss of telomerase activity in alternative lengthening of telomere (ALT) systems are discussed. We propose that elongation of minisatellite repeats using recombination/replication processes initially substitutes for the loss of telomerase function. Then in more established ALT groups, subtelomeric satellite repeats may replace the telomeric minisatellite repeat whilst maintaining the recombination/replication mechanisms for telomere elongation. Thereafter a retrotransposition-based end-maintenance system may become established. The influence of changing sequence motifs on the properties of the telomere cap is discussed. The DNA and protein components of telomeres should be regarded--as with any other chromosome elements--as evolving and co-evolving over time and responding to changes in the genome and to environmental stresses. We describe how telomere dysfunction, resulting in end-to-end chromosome fusions, can have a profound effect on chromosome evolution and perhaps even speciation.