Transthyretin (TTR) is a tetrameric protein synthesized mostly by the liver. As a result of gene mutations or as an ageing-related phenomenon, TTR molecules may misfold and deposit in the heart and in other organs as amyloid fibrils. Amyloid transthyretin cardiac amyloidosis (ATTR-CA) manifests typically as left ventricular pseudohypertrophy and/or heart failure with preserved ejection fraction and is an underdiagnosed disorder affecting quality of life and prognosis. This justifies the current search for novel tools for early diagnosis and accurate risk prediction, as well as for safe and effective therapies. In this review we will provide an overview of the main unsolved issues and the most promising research lines on ATTR-CA, ranging from the mechanisms of amyloid formation to therapies.