Modern wearable IoT devices enable the monitoring of vital parameters such as heart or respiratory rates (RESP), electrocardiography (ECG), photo-plethysmographic (PPG) signals within e-health applications. However, a common issue of wearable technology is that signal transmission is powerdemanding and, as such, devices require frequent battery charges and this poses serious limitations to the continuous monitoring of vitals. To ameliorate this, we advocate the use of lossy signal compression as a means to decrease the data size of the gathered biosignals and, in turn, boost the battery life of wearables and allow for fine-grained and long-term monitoring. Considering one dimensional biosignals such as ECG, RESP and PPG, which are often available from commercial wearable IoT devices, we provide a throughout review of existing biosignal compression algorithms and introduce novel approaches based on online dictionaries, elucidating their operating principles and providing a quantitative assessment of their compression, reconstruction and energy consumption performance. As we quantify, the most efficient schemes allow reductions in the signal size of up to 100 times, which entail similar reductions in the energy demand, by still keeping the reconstruction error within 4% of the peak-topeak signal amplitude. Avenues for future research are finally discussed.