Genetic material derived from tumours is constantly shed into the circulation of cancer patients both in the form of circulating free nucleic acids and within circulating cells or extracellular vesicles. Monitoring cancer-specific genomic alterations, particularly mutant allele frequencies, in circulating nucleic acids allows for a non-invasive liquid biopsy for detecting residual disease and response to therapy. The advent of molecular targeted treatments and immunotherapies with increasing effectiveness requires corresponding effective molecular biology methods for the detection of biomarkers such as circulating nucleic acid to monitor and ultimately personalise therapy. The use of polymerase chain reaction (PCR)-based methods, such as droplet digital PCR, allows for a very sensitive analysis of circulating tumour DNA, but typically only a limited number of gene mutations can be detected in parallel. In contrast, next-generation sequencing allows for parallel analysis of multiple mutations in many genes. The development of targeted next-generation sequencing cancer gene panels optimised for the detection of circulating free DNA now provides both the flexibility of multiple mutation analysis coupled with a sensitivity that approaches or even matches droplet digital PCR. In this review, we discuss the advantages and disadvantages of these current molecular technologies in conjunction with how this field is evolving in the context of melanoma diagnosis, prognosis, and monitoring of response to therapy.