This question could seem pretty common but I want to give it a different take.
As an undergraduate student, for estimation of parameters I was taught about the glorified Maximum Likelihood and Least Squares methods, that are very useful for many properties they yield. For instance, a strong factor for which people choose MLE is that it gives asymptotically efficient estimations.
I know there are historically a variety of alternative method, but what I am looking for are ones that currently find a niche of usage as better choices, not just for textbook-only never-used examples.
Also I wouldn't mind a not too in-depth answer, if the field of usage is clear for someone to further research for other informations and the advantages over the above mentioned methods are clearly described. It is also totally fine for different answers to add just one or two methods.
EDIT: I am mainly interested in non-Bayesian statistics that arise from physical experiments (projects on large scale such as CERN projects) or economic studies.