This paper focuses on our solutions of filters with high frequency selectivity, extended stop- band, and dual-band operation functions, by means of exploiting the unique properties of composite resonators. First, filters using composite resonators to produce multiple transmission zeros are described. As no cross-coupling between non-adjacent resonators is required, the filters are easy to design and implement. Next, to improve the inherent poor stopband property of this type of filters, new filters integrating both composite resonators and conventional resonators are devised. Finally, dual-band bandpass filters and dual- band bandstop filters with controllable dual-band responses are realized in novel and compact microstrip configurations. All these filters are designed based on novel lumped-element filter circuits incorporating composite resonators, and all the element values of the circuits are determined readily by using our derived closed-form formulas. A number of example filters are provided, and their measured characteristics show good agreements with theoretical predictions.