This study explores the dynamic return and volatility connectedness for some dominant industrial (Aluminium, Copper, Lead, Nickel, Tin, and Zinc) and precious metals (Gold, Palladium, Platinum, Silver) to crude oil shocks (risk, demand, and supply) during the sample period between January 2, 2009 and July 17, 2020. Our findings indicate that, demand shocks and risk shocks are the dominant receiver (transmitter) of shocks from (to) for metal returns. Second, we document the time-varying nature of both total return and volatility connectedness. Third, both net directional return and volatility connectedness show that some metals such as Tin, Gold and, even, Nickel, Lead and Aluminium appear as net transmitters, at least in some intervals of the sample period analysed. On the other hand, other industrial and precious metal markets show a net receiver profile, such as Copper, Zinc and Platinum, among others. Lastly, we find more differences between the net dynamic connectedness of the metal markets analysed in terms of return than volatility. The net directional volatility connectedness increases sizably during the global crisis due to the spread of the SARS-CoV-2 coronavirus.