This is a phase 1, multicenter, open-label trial to evaluate the safety of talimogene laherparepvec, injected intrahepatically, into liver tumors with known progression in subjects with Hepatocellular carcinoma and subjects with liver metastases from breast adenocarcinoma, colorectal adenocarcinoma, gastroesophageal cancer (adenocarcinoma or squamous cell carcinoma), melanoma, non-small cell lung cancer, or clear cell renal cell carcinoma. The study consists of 2 parts and 2 groups. Part 1 is a 3+3 dose escalation consisting of 3 sequential dose cohorts each administering talimogene laherparepvec in increasing dose concentrations and dose volumes. In Part 1, the Maximum Tolerated Dose determination of non-hepatocellular carcinoma liver metastases (Group A) will be evaluated separately from hepatocellular carcinoma (Group B), and each dose cohort will need to be deemed safe for non-hepatocellular carcinoma subjects before it will be administered in hepatocellular carcinoma subjects. Part 2 consists of expansion cohorts administering the Maximum Tolerated Dose of talimogene laherparepvec determined from Part 1 for Groups A (non-hepatocellular carcinoma) and B (hepatocellular carcinoma) to approximately 10 subjects for each tumor type.