$L_{\mathrm{\infty }}$ and $A_{\mathrm{\infty }}$ structures: then and now

Looking back over 55 years of higher homotopy structures, I reminisce as I recall the early days and ponder how they developed and how I now see them. From the history of $A_{\mathrm{\infty }}$-structures and later of $L_{\mathrm{\infty }}$ -structures and their progeny, I hope to highlight some old results which seem not to have garnered the attention they deserve as well as some tantalizing new connections.