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Radio pulsars are rotating neutron stars (NSs) identified by a periodic detection of radio emission with intervals of seconds to milliseconds. The periodicity of the emission is closely tied to the NS’s spin frequency such that timing a pulsar allows its spin frequency to be accurately determined. The spin frequency is generally predictable except for the case of two timing irregularities: glitches and timing noise. Both represent phenomena that occur on different time-scales with glitches affecting short-term evolution and timing noise affecting long term evolution. Glitches are sudden increases in the spin frequency which is sometimes followed by a post-glitch recovery. Timing noise is the term used for the residuals left over after the predictable spin evolution is subtracted from observations. There are existing models that can explain glitches, their recovery as well as timing noise, but in this thesis, we focus on creating two more, one for the post-glitch recovery and another for timing noise. The key aspect of these models is their connection to gravitational waves (GWs), which is an idea not well explored. In the first part of this thesis, we create the “transient mountain” model which can explain post-glitch recoveries and make falsifiable predictions for the GWs that come off. This is based off the idea that a NS “mountain” would create an extra braking torque on the NS, hence, spinning it down during the post-glitch recovery. For the second part of this thesis, we create a model for timing noise which we propose is caused by successive (micro)glitches which cause the NS to oscillate. These glitches excite the f-modes on the NS which are known to emit GWs. In …