This paper examines the spillovers of return and volatility transmitted from fossil energies (crude oil and natural gas) and several important financial variables (stock market index, bonds, and the volatility index) to renewable stock markets in the US and Europe under the time-frequency domain frameworks. The total spillovers of return and volatility from all variables to renewable stock markets in the US are higher than those in Europe. Stock markets transmit the highest return spillovers to renewable energy stocks, which far exceed the spillovers from fossil energy to renewable energy stocks in both regions. In addition, both return and volatility spillovers could be enhanced, possibly due to specific events or sudden changes in prices. In particular, extreme events such as the Brexit referendum in 2016 influenced mostly the volatility spillovers across European markets. Moreover, the spillovers of return and volatility are contingent on frequency, and most return spillovers are concentrated at the high frequency, whereas most volatility spillovers are concentrated at the low frequency. These results remind investors that it is necessary to consider the investment horizon when making their financial decisions on renewable energy investment.