Nanographene structures consisting of diradical π-conjugated hydrocarbons are predicted to have high-spin ground states which consequently attracted much research attention for their potential applications in molecular spintronics. Nanographenes such as heptauthrene and triangulene are diradicals with high chemical reactivity and difficult to synthesize. Here, we discuss the progress in experiments and use first-principles calculations to investigate the electronic and magnetic properties of heptauthrene and triangulene in freestanding and metal-substrate-supported systems. First-principles investigations are essential in providing a guide in the synthesis of nanographene structures for spintronics and quantum technology applications.