We present a combined study of zero-field (51) V and I-127 NMR at ambient pressure and specific heat and magnetization measurements under pressure up to 2.08 GPa on bulk single crystals of the van der Waals ferromagnet VI3. At ambient pressure, our results consistently demonstrate that VI3 undergoes a structural transition at T-s approximate to 78 K, followed by two subsequent ferromagnetic transitions at T-FM1 approximate to 50 K and T-FM2 approximate to 36 K upon cooling. At lowest temperature (T < T-FM2), two magnetically ordered V sites exist, whereas only one magnetically ordered V site is observed for T-FM1 < T < T-FM2. Whereas T-FM1 is almost unaffected by external pressure, T-FM2 is highly responsive to pressure and merges with the T-FM1 line at p 0.6 GPa. At even higher pressures (p approximate to 1.25 GPa), the T-FM2 line merges with the structural transition at T-s which becomes moderately suppressed with p for p < 1.25 GPa. Taken together, our data point toward a complex magnetic structure and an interesting interplay of magnetic and structural degrees of freedom in VI3.