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The shape and diversity of dwarf galaxy rotation curves is at apparent oddswith dark matter halos in a $\Lambda$ Cold Dark Matter ($\Lambda$CDM)cosmology. We use mock data from isolated dwarf galaxy simulations to show thatthis owes to three main effects. Firstly, stellar feedback heats dark matter,leading to a 'coreNFW' dark matter density profile with a slowly risingrotation curve. Secondly, if close to a recent starburst, large HI bubbles pushthe rotation curve out of equilibrium, deforming the rotation curve shape.Thirdly, when galaxies are viewed near face-on, their best fit inclination isbiased high. This can lead to a very shallow rotation curve that falselyimplies a large dark matter core. All three problems can be avoided, however,by a combination of improved mass models and a careful selection of targetgalaxies. Fitting our coreNFW model to mock rotation curve data, we show thatwe can recover the rotation curve shape, dark matter halo mass $M_{200}$ andconcentration parameter $c$ within our quoted uncertainties.  We fit our coreNFW model to real data for four isolated dwarf irregulars,chosen to span a wide range of rotation curve shapes. We obtain an excellentfit for NGC 6822 and WLM, with tight constraints on $M_{200}$, and $c$consistent with $\Lambda$CDM. However, IC 1613 and DDO 101 give a poor fit. ForIC 1613, we show that this owes to disequilibria and its uncertain inclination$i$; for DDO 101, it owes to its uncertain distance $D$. If we assume $i_{\rmIC1613} \sim 15^\circ$ and $D_{\rm DDO101} \sim 12$ Mpc, consistent withcurrent uncertainties, we are able to fit both galaxies very well. We concludethat $\Lambda$CDM appears to give an excellent match to dwarf galaxy rotationcurves.

Understanding the shape and diversity of dwarf galaxy rotation curves in LCDM