This study applies a set of measures developed by Diebold and Yilmaz (2012, 2016) to examine connectedness via return and volatility spillovers across six large cryptocurrencies from August 7, 2015 to February 22, 2018. Regardless of the sign of returns, the results show that Litecoin and Bitcoin are at the centre of the connected network of returns. This finding implies that return shocks arising from these two cryptocurrencies have the most effect on other cryptocurrencies. Further analysis shows that connectedness via negative returns is largely stronger than via positive ones. Ripple and Ethereum are the top recipients of negative-return shocks, whereas Ethereum and Dash exhibit very weak connectedness via positive returns. Regarding volatility spillovers, Bitcoin is the most influential, followed by Litecoin; Dash exhibits a very weak connectedness, suggesting its utility for hedging and diversification opportunities in the cryptocurrency market. Taken together, results imply that the importance of each cryptocurrency in return and volatility connectedness is not necessarily related to its market size. Further analyses reveal that trading volume and global financial and uncertainty effects as well as the investment-substitution effect are determinants of net directional spillovers. Interestingly, higher gold prices and US uncertainty increase the net directional negative-return spillovers, whereas they do the opposite for net directional positive-return spillovers. Furthermore, gold prices exhibit a negative sign for net directional-volatility spillovers, whereas US uncertainty shows a positive sign. Economic actors interested in the cryptocurrency market can build on our findings when weighing their decisions.