The present era of precision medicine sees 'cancer' as a consequence of molecular derangements occurring at the commencement of the disease process, with morphologic changes happening much later in the process of tumorigenesis. Conventional imaging techniques, such as computed tomography (CT), ultrasound, and magnetic resonance imaging (MRI), play an integral role in the detection of disease at a macroscopic level. However, molecular functional imaging (MFI) techniques entail the visualisation and quantification of biochemical and physiological processes occurring during tumorigenesis, and thus has the potential to play a key role in heralding the transition from the concept of 'one size fits all' to 'precision medicine'. Integration of MFI with other fields of tumour biology such as genomics has spawned a novel concept called 'radiogenomics', which could serve as an indispensable tool in translational cancer research. With recent advances in medical image processing, such as texture analysis, deep learning, and artificial intelligence (AI), the future seems promising; however, their clinical utility remains unproven at present. Despite the emergence of novel imaging biomarkers, a majority of these require validation before clinical translation is possible. In this two-part review, we discuss the systematic collaboration across structural, anatomical, and molecular imaging techniques that constitute MFI. Part I reviews positron emission tomography, radiogenomics, AI, and optical imaging, while part II reviews MRI, CT and ultrasound, their current status, and recent advances in the field of precision oncology.