Can RemoteFunction fire to all clients?

It will not make sense to have RemoteFunction have some sort of InvokeAllClients() function. Since RemoteFunctions have to return something, how would the script store and process the result from multiple clients?

You're better off invoking it for each client manually. To prevent one invoke from blocking another, you can wrap each call in a spawn():

-- In a server script
for _, player in pairs(game:GetService("Players"):GetPlayers()) do
    spawn(
        function()
            local returnVal = RemoteFunction():InvokeClient(player, arguments)
            -- process returnVal here
        end
    )
end

Hi! As Far as I know yes, RemoteFunctions can fire to all Clients...RemoteFunctions and RemoteEvents are both very Similiar, but the main and biggest difference is that in Remote Functions not only can the Server "Fire" to the Client, the Client can also "call back" and give a message back in the same Remote Function...But, Despite what you said about the lag...it is recommended that you use RemoteEvents over RemoteFunction, unless you need the Client or the Server to call back in the same Function.. More information over Remote Funtions here- http://wiki.roblox.com/index.php?title=API:Class/RemoteFunction Remote Functions also use the onClientInvoke instead of the onClientEvent like the RemoteEvent.. Hope this helped! Let me Know if it did! The Wiki has a lot more helpful information about this, check there!